5

(a) Multiple Choice:Suppose lim f (x) = 7and |f(x)_7 < 0.25 whenever 9.75 <x <l1. X-10 Then If(r)-7<0.25 whenever Ix-10/ < & if & equals 0.25...

Question

(a) Multiple Choice:Suppose lim f (x) = 7and |f(x)_7 < 0.25 whenever 9.75 <x <l1. X-10 Then If(r)-7<0.25 whenever Ix-10/ < & if & equals 0.25; 0.5 0.75sin(x _1) (b) Find the limit: lim- X1 x+r-2

(a) Multiple Choice: Suppose lim f (x) = 7and |f(x)_7 < 0.25 whenever 9.75 <x <l1. X-10 Then If(r)-7<0.25 whenever Ix-10/ < & if & equals 0.25; 0.5 0.75 sin(x _1) (b) Find the limit: lim- X1 x+r-2



Answers

$\lim _{x \rightarrow 0} \frac{e^{x}-e^{-x}+2 \sin x+x^{3}-4 x}{10 x^{3}}$ is (a) $\frac{1}{5}$ (b) $\frac{1}{20}$ (c) $\frac{1}{10}$ (d) $\frac{1}{15}$

Problem that this limit as access to zero of irresponsible X minus negative or negative X plus twice a sign X plus X cubed minus four X over. Then X cubed as this is an indeterminate form. That is the limit is 0- zero form. We'll use the la capitals rule with states limit of effects of a G X as X tends to zero is a flash X over G dash X. If limited effects as extends to zero and zero and limited G X as X tends to zero is also zero. So let us use the capital's rule for finding the limit of the function. So let us find the derivative of the numerator which is it is super X plus it is to the part of negative of eggs plus twice of because six last three times of X squared minus four or what? 30 times of x square as this is again, is an indeterminate form. So we'll again use the capital's rule which give us limit of it as X tends to zero of it. Hispanics negative response negative affects minus twice of cynics Plus six times of weeks. For what? 16 times of X? Again, this is an indeterminate forms. Will again apply the law. Capitals route To obtain. The limited extends to zero of Paris panics plus it is super negative of fixed minus twice. Off course six plus six. What 60 now? This is not an indeterminant form. We can apply the limit in this function to obtain It is 10 plus it is a negative of zero minus twice of consider. Oh that's six over 60. Which on simplification we will get one this one -2-plus 6/16, which is equal into 1/10. So we can see that the correct option is option C. That is one or what then, is the limit of the given function.

Yeah, we have to make the developed the values of function at x equals two minus 20.1 minus part 1000.1 and 0.1. And for the part of the user table to estimate the limitations you know of effects effects is given. Yeah. Sign off five x upon X. Okay. Mhm. Then Actually cause to -4.1 The value of this function will because your 4.794 and the value of X. The cost 2.1. The value of this function will be caused to 4.794. When the value of dysfunction, the question point minus of 0.0.0 point 01 So this will be close to 4.99? Yes. Okay then Actually equal to this value will because you 4.997. All right. No, this is the party for the part We we have to use the stable to estimate the limit extends to zero of effects. It was a part of me. We have to find the limit Extends to zero FX. So the limit is exist then is then left and limit. So because to write and limit at extends to zero so last time limit will be close to limit Extends to 0- of FX on the table. You can see that When excess approaches to the zero from the left, The value of the function is about to 4.997. That is the cost of four 997 That is about five. Okay. When the limit extends to zero plus one actually approaches to the approaches to the zero from the right, The value of the function is about to 4.997. That is about 25 L h l h l equal in it. That is the question. Five. So the value of this limited will be cost to five. So this is that And so I hope to an issue thank you.

Everybody. Okay, so we're doing Chapter two, Section three. Problem number 42. So we're dealing in the world of limits. So we're preparing toe do derivatives and calculus and all that. And so this problem gives you a function. F of X is equal to X squared minus two to the X over 1000. That's the function that looks like something. It has some sort of graph, right? X squared. Just looks like a problem to you. Minus two d x over 1000. So it'll look very similar to a problem, but something will be messed up. And so you have to find Well, we call it the limit of F of X. And so basically the way you'd read. Ah, the thing on the right side is you'd find the limit of f of X as X approaches zero. So basically, X equals zero. Think that's the point, Right? Some value of X. And you want to know what, uh, what the output is at that point, it might be it might be a number. It might be just continuous. Maybe there's a vertical asking toad or something. So in this problem, specifically, they have you Ah, trying to find a bunch of points, right? They say, you know, for like, you know, for X equals one this a You know, what is what is f of X And, you know, you can go, uh, plug it into a calculator. You could work it out if you so choose and, you know, you get you get the number about, like, point a 0.0.9 90 something like that. And then you do some other ones they ask you to do 0.8. Ah, and you know, we'll just do a sketch of it, But pointing a that yields you Ah, 0.6, 338 and the whole point of this right, You have X equals one, and then your 10.8 on the 0.6 point 4.2 point one. You see, I was getting closer to that X value of zero that we want. We start on the right side. You could have also started on the left. I like negative values, but we're starting values of X. And we're getting closer and closer and closer to zero and trying to find out what this FX. Maybe it's approaching some number. That's kind of what we're hoping for. So it's 0.8. That's 0.63 He will jump down a few values. The values were just supposed to help you get context. So a point, too. You know, you plug this into the, you know, to the function. That's not really the hard part here. The easy part is the algebra. You just plug it in and find out what the values. Its point. 038 That's much closer. Thio, Um, no to zero. So you have, like, that's almost one that's nearing 10.5, but they were getting really close to zero. So then you think, like, Okay, maybe we did below zero like it kind of feels like it approaching zero. Right? It was that almost one. And then and then that you eventually the very last one. They ask you to do this point. 05 on that point, 01 that makes me feel like it's not going to go below zero. There were some it in between, right? But if I had to take a guess, right? And if they find the limited that thing right, tell me What What's the output at tactical zero based on the way that this trend is going right? I don't actually know. Autograph. Looks like it probably looks something like a problem, but I don't know, 100% right? This this Ah, this part, um right here kind of messes with me, right? And so I I would guess zero. And that's what partner wants you to do. Part A just says, hey, takes on values 1.8 point two. All that stuff and just kind of gave me an idea that what you think it would be My guess is zero because it went 00.98 point 63.38 We're getting really close to 0.1 That's a very close to zero. And then point b of this thing is just trying to give you an even better understanding so that you can start to reassure yourself. Right? Then you get into numbers like 0.4 And then that ends up being really small. It's even smaller than 0.1, and then you get numbers like 0.3 and we're literally in tow, like it's like point. Oh, uh, like fourth, it's like it's very, very small. So after you do enough of those, right, you plug in point over 3.1 after doing a few of those. You really get an idea? That s Q. Hey, try to do another guest. Maybe you didn't guess here. Oh, that's okay. But after doing this, it really reassures you that delivered of this thing is zero Hope this helps until next time.

So we want to find the limit of this function as X approaches for. Uh and we're going to do that by factoring the numerator and factoring the denominator and then seeing if we can cancel some factors. Uh and then we're going to repeat that process for this function down here. After we calculate the limit of this function as X approaches for we'll look at its graph and see if it confirms our limit and then we'll do the same thing for this problem down here. Uh So now we're gonna factor the numerator and the denominator uh in each of these functions. Okay, define the limit of this function as X approaches four. We factored the numerator and we factored the denominators three, X squared minus 10. Next month is eight is equal to 32 times x months for and five X squared plus 16 next minus 16 factors into five X minus four times X plus four. So we need to take the limit of this function as X approaches four. Uh Well, let's see what happens as X approaches for X-plus four will approach eight As X approaches 45 times x -4 will approach five times 4 -4, which is 16. As X approaches four for -4 will approach zero and the three X plus two terms as extra approaches 43 X plus two will approach three times four plus two, which is 14. So we see the numerator is going to approach 14 times zero. So the entire numerator Is going to approach 14 Times zero, which is zero. The entire denominator Is going to approach 16 times eight. Let's see what that is real quick. The entire denominator is going to approach 1 28. So as X is approaching for the numerator is approaching zero, the denominator is approaching 1 28. And the entire expression, the entire function is approaching zero, divided by 1 28. Well, zero divided by 1 28 will just be zero. Uh So the limit of this function as X approaches for is zero. Now, let's confirm that graphically. So here's the graph of the function and as excellent zoom in a little bit. As X is approaching for, we expect this function to be approaching zero and you can see that's exactly what's happening. Okay. As X approaches four From the right side, two functions going close to zero. As X approaches for from the left side of four to function values are going close to zero. Now, let's find a limit of this function written in blue. As X approaches for, we factored the numerator into five, X minus six times X minus four. We factor the denominator into four, X plus five times X minus sport. Since we're taking the limit as X approaches four, X does not actually end up equaling four. We can cancel out the X -4 factors because they won't be zero because X will not be equaling for. So we need to just simply take the limit of the Romanian expression as X approaches for. Well five times X minus six will approach five times four minus six as X approaches four, So five times 4 -6 is 20-6 or 14. So the numerator is approaching 14 as X approaches for the denominator four, X plus five. As extra approaches for four, X plus five approaches four times four plus five, which is 16 plus five, which is 21. So the denominator approaches 21 as X approaches four. And so this close ocean approaches the limit of 14/21, Which can reduce be reduced to 2/3. So the limit of this function as X approaches for Is 2/3. Let's confirm geographically. All right, so we graph we are graphing dysfunction and as x approaches for, we expect the function values to be approaching two thirds, which which would be approximately .67. So as X is moving towards four from the left side, you can see that the function values are getting closer uh 2.67. And as uh to function As X is approaching for from the left side, you can see the function values are getting closer once again 2.67. And so the limit of dysfunction as x approaches for is 2/3.


Similar Solved Questions

5 answers
Draw the expected recciver operation characteristic (ROC) curve for three cases of data distribution
Draw the expected recciver operation characteristic (ROC) curve for three cases of data distribution...
5 answers
Prove that the following relations do not satisfy the stated property. (4) (5 points) on N not symmetric (b) points) on Nis not transitive (c) points) Let R be the relation on N defined 43 aRb + 5Mla + 6)Show R is not reflexive:
Prove that the following relations do not satisfy the stated property. (4) (5 points) on N not symmetric (b) points) on Nis not transitive (c) points) Let R be the relation on N defined 43 aRb + 5Mla + 6) Show R is not reflexive:...
5 answers
5 Let X1 , - DefineXn be a random sample from N ( L , 02) distribution:X= 1E-1X and 52 = Ei-1(Xi - X)2 . n-1What is the distribution of (justify your answer):a)X)b)(n-1) s2/2 Ei-1(Xi - X )?/a?c) Ei-1(Xi _ p )/a? ,d) T= (X- p) / (Svn) _
5 Let X1 , - Define Xn be a random sample from N ( L , 02) distribution: X= 1E-1X and 52 = Ei-1(Xi - X)2 . n-1 What is the distribution of (justify your answer): a) X) b) (n-1) s2/2 Ei-1(Xi - X )?/a? c) Ei-1(Xi _ p )/a? , d) T= (X- p) / (Svn) _...
5 answers
Question 3Not yet answeredMarked out of 1.50~Flag questionShow thatcos Xsin x is the solution ofthe differential equation cot x
Question 3 Not yet answered Marked out of 1.50 ~Flag question Show that cos Xsin x is the solution ofthe differential equation cot x...
5 answers
Uontsane 26 points)341 loitisiste the Notice blank then negative corresponding that the JH DNE Ihen insc J insert = doseed Otherwise, 3 blank INF line = 3 unit H on the numibeoies graph:Determine lim 2 1 given by the following graphSaved
uontsane 26 points) 341 loitisiste the Notice blank then negative corresponding that the JH DNE Ihen insc J insert = doseed Otherwise, 3 blank INF line = 3 unit H on the numibeoies graph: Determine lim 2 1 given by the following graph Saved...
5 answers
Shn 0Ces.0 du2 * 1 0 sinz Ax
shn 0 Ces.0 du 2 * 1 0 sinz Ax...
5 answers
4) Evaluate $ (3 + sin(x + y)) dS where C is the path from (0,0) to (2,4).
4) Evaluate $ (3 + sin(x + y)) dS where C is the path from (0,0) to (2,4)....
5 answers
A force F8 i - 5j) Nacts on particle that undergoes displacement AF = (2i+))= Find the work done by the force on the particle_(b) What is the angle between F and Ar?
A force F 8 i - 5j) Nacts on particle that undergoes displacement AF = (2i+))= Find the work done by the force on the particle_ (b) What is the angle between F and Ar?...
5 answers
Add a FileRecord AudioRecord VideoQuestion 10 (2 points)Write the equation of the function f(x)-2* after the following transformations are applied to it: g(x)-3f(-2x+2)-2. Use the equation editor to type your final answer_
Add a File Record Audio Record Video Question 10 (2 points) Write the equation of the function f(x)-2* after the following transformations are applied to it: g(x)-3f(-2x+2)-2. Use the equation editor to type your final answer_...
5 answers
In the following exercises, evaluate each expression for the given values.$8-y$ when(a) $y=3$ ( b ) $y=-3$
In the following exercises, evaluate each expression for the given values. $8-y$ when (a) $y=3$ ( b ) $y=-3$...
5 answers
The gravitational force between two objects is 8 N. If thedistance between the objects is doubled, what is the resultingmagnitude of the gravitational force?Group of answer choices16 N12 N4 N2 NNone of the above.
The gravitational force between two objects is 8 N. If the distance between the objects is doubled, what is the resulting magnitude of the gravitational force? Group of answer choices 16 N 12 N 4 N 2 N None of the above....
5 answers
Find a cofunction with the same value as the given expression: cos(5 +x)[-/0.08 Points]DETAILSOSPRECALC1 7.2.074_Find & cofunction wlth the same value as thle glven expression30 cos
Find a cofunction with the same value as the given expression: cos(5 +x) [-/0.08 Points] DETAILS OSPRECALC1 7.2.074_ Find & cofunction wlth the same value as thle glven expression 30 cos...
5 answers
(9) (a) Determine whether the given sequence is convergent Or divergent:01 = 1,@n+41 =4 - an(b) What happens if the first term is 41 = 27(10) For what values of b is the following sequence convergent? Gn = n . 6"
(9) (a) Determine whether the given sequence is convergent Or divergent: 01 = 1, @n+41 =4 - an (b) What happens if the first term is 41 = 27 (10) For what values of b is the following sequence convergent? Gn = n . 6"...
5 answers
Question 1Let F = r? 7+2ry Jbe a vector feld on the plane At the given point (1, -1}, the curl density is cqual to|and thc divergence i5equal toQuestion 2HAsWnchrtencnt / true aboui Grcen s throron; A lt idennfes the circulation ' Mleiini ef divereenc ol Eur] density:Wdentincs tnc Tux with the integrai2 # ocnntestng circulation wlth ngal didivtsenteentifies the tlux witn (nc2 pts
Question 1 Let F = r? 7+2ry Jbe a vector feld on the plane At the given point (1, -1}, the curl density is cqual to| and thc divergence i5 equal to Question 2 HAs Wnchrtencnt / true aboui Grcen s throron; A lt idennfes the circulation ' Mleiini ef divereenc ol Eur] density: Wdentincs tnc Tux w...
5 answers
Wtich of the followicg Folzr equationg Lest deccribeg thiz curve?7=1+3in87=1-3n87=1+0238T=l_ 313 $(F) Nocz of tLz 2kcve
wtich of the followicg Folzr equationg Lest deccribeg thiz curve? 7=1+3in8 7=1-3n8 7=1+0238 T=l_ 313 $ (F) Nocz of tLz 2kcve...
5 answers
32 -2 72 point) The matrix C = 21 -6 41 -16 -36 has two distinct eigenvalues, ^1 12: 1] has multiplicity The dimension of the corresponding eigenspace is 12 has multiplicity The dimension of the corresponding eigenspace is Is the matrix diagonalizable? (enter YES or NO)
32 -2 72 point) The matrix C = 21 -6 41 -16 -36 has two distinct eigenvalues, ^1 12: 1] has multiplicity The dimension of the corresponding eigenspace is 12 has multiplicity The dimension of the corresponding eigenspace is Is the matrix diagonalizable? (enter YES or NO)...

-- 0.025842--