5

Find the domain of the following vector-valued functions: #(t) = (sin 2t)i +7_Ji+(-o) #(t) = Indt-1)i + jtek t-4 7() = V3-21-71+ej+ k...

Question

Find the domain of the following vector-valued functions: #(t) = (sin 2t)i +7_Ji+(-o) #(t) = Indt-1)i + jtek t-4 7() = V3-21-71+ej+ k

Find the domain of the following vector-valued functions: #(t) = (sin 2t)i +7_Ji+(-o) #(t) = Indt-1)i + jtek t-4 7() = V3-21-71+ej+ k



Answers

Find the domain of the vector-valued function. $$\mathbf{r}(t)=\sin t \mathbf{i}+4 \cos t \mathbf{j}+t \mathbf{k}$$

Let's find the domain of the following vector Valued function. R t equals co signed to T I, plus each of the square root of T J plus two over tea. Hey, well, the domain off a vector. Higher valued function is the intersection of the domains of all the component functions. Just find the domains of each of the component functions. First, we have the co sign of two t. The domain of the coastline of two t is all real numbers. There are no restrictions for what we can plug into T. The second component function the to the square root of tea. I can play anything into the exponential function, but to take the square root, I must have a non negative number. And so all non negative numbers. Zero to infinity is the domain of the second component function, because that's what I can use in the square root in the third component function. 12 over tea. It is all real numbers except for zero. So it's everything except T zero well to satisfy all three of those, the first component function doesn't have any influence. It's these two. This tells us that I have to have a non negative number. This tells us, additionally, that the number can't be zero and said the domain for arms, higher function numbers that I complainant All three component functions are just positive numbers. So the domain of this function is positive numbers open and for semi infinite open interval from zero to infinity set of all Xs X is greater than zero.

To find the domain for a vector, we have to look at all the components separately and then pick the domain. That is the most constrictive. So Ellen of T. Remember Ellen has a a Centobie at T equals zero and can't be negative. So T does have to be greater than zero for RJ component. There's no constraints. So all real numbers at the same with our K. So we have to go with that. Tea has to be greater than zero. So I'm going to write in my interval notation from zero to infinity.

We're asked to find the domain of the vector valued function. So what we're gonna do is we're going to look at each of its components and we are going to choose the domain that is most restrictive. So for example are I component. We need to make sure that anything that is inside our square root Is greater than your equal to zero. So we can say that T square better be less than or equal to four. And then when we take the square root of both sides we get the absolute value of T. Must be less than or equal to two. So that puts us between negative two and two. Now our other two pieces are any. Any value can go into my J. R. K. So that stands for the R. With the two slashes to infer all real numbers. So our most control points constrained um component is my ex component. So are domain of our vector valued function is going to be all values between negative two and two. And you can put that either in um interval notation or however you want to state that

Here. We want to find the domain so the denominator cannot equals zero. So 70 plus three equals 0 70 equals Negative. Three t cannot equal two negatives. 3/7. So our domain is negative. Infinity to negative. 3/7. And from negative 3/7 to infinity.


Similar Solved Questions

5 answers
What oxygen-containing functional group the most acidic and why?
What oxygen-containing functional group the most acidic and why?...
5 answers
(10 points) Suppose object isat 30. front of spherical lens that has tocal length of 40.0 cm Where image ocated? What are the magnification and the character of the irnage? Draw ray diagram. Object begins slide toward lens, how fast does the object move_ If Image velocity is Vc-5 m/s? (show step by step solution)
(10 points) Suppose object isat 30. front of spherical lens that has tocal length of 40.0 cm Where image ocated? What are the magnification and the character of the irnage? Draw ray diagram. Object begins slide toward lens, how fast does the object move_ If Image velocity is Vc-5 m/s? (show step by ...
5 answers
Based on collision theory, explain which molecular-level factors influence whether collision between two molecules will lead to reaction_
Based on collision theory, explain which molecular-level factors influence whether collision between two molecules will lead to reaction_...
5 answers
For the circuit belov find Reqr the current through Ry (I3) the current throughRz (I,2).R, - 17 QR = 15 0Rz = 12 0Vo = 39 VRt4
For the circuit belov find Reqr the current through Ry (I3) the current through Rz (I,2). R, - 17 Q R = 15 0 Rz = 12 0 Vo = 39 V Rt4...
5 answers
Use the following graph of the function y = f(x) to find the values, if possible Estimate when necessary:a.)lim_ f(x)lim , f(x) X~otlim f(x) "-0limf(x)lim; Rf(r)Evaluace %he following Ilmlts, or If appropriate, explain why It does not exlst: Jima 4BI
Use the following graph of the function y = f(x) to find the values, if possible Estimate when necessary: a.) lim_ f(x) lim , f(x) X~ot lim f(x) "-0 limf(x) lim; Rf(r) Evaluace %he following Ilmlts, or If appropriate, explain why It does not exlst: Jima 4BI...
1 answers
Case Study: Consider the data set for Exercise 12.12, page 472 (hospital data), repeated here. $$ \begin{array}{rrrrrrr} \text { Site } & x_{1} & x_{2} & x_{3} & x_{4} & x_{5} & y \\ \hline 1 & 15.57 & 2463 & 472.92 & 18.0 & 4.45 & 566.52 \\ 2 & 44.02 & 2048 & 1339.75 & 9.5 & 6.92 & 696.82 \\ 3 & 20.42 & 3940 & 620.25 & 12.8 & 4.28 & 1033.15 \\ 4 & 18.74 & 6505 & 568.33 & 36.7 & 3.
Case Study: Consider the data set for Exercise 12.12, page 472 (hospital data), repeated here. $$ \begin{array}{rrrrrrr} \text { Site } & x_{1} & x_{2} & x_{3} & x_{4} & x_{5} & y \\ \hline 1 & 15.57 & 2463 & 472.92 & 18.0 & 4.45 & 566.52 \\ 2 & 44...
5 answers
Decide whether each statement is true or false.$$-|-28|=28$$
Decide whether each statement is true or false. $$ -|-28|=28 $$...
5 answers
Physics: Uniform Motion A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat travels upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current? See the figure.
Physics: Uniform Motion A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat travels upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current? See the figure....
5 answers
SET-UP Do_Not Evaluate an iterated triple integral in Spherical coordinates to find the volume of the solid lying inside of the sphere, x2 + y2+22 =25 and inside(above) the cone 3z = Vx2 y2
SET-UP Do_Not Evaluate an iterated triple integral in Spherical coordinates to find the volume of the solid lying inside of the sphere, x2 + y2+22 =25 and inside(above) the cone 3z = Vx2 y2...
1 answers
Find the area of the following triangles $T$. The sides of $T$ are $\mathbf{u}=\langle 3,3,3\rangle, \mathbf{v}=\langle 6,0,6\rangle,$ and $\mathbf{u}-\mathbf{v}$
Find the area of the following triangles $T$. The sides of $T$ are $\mathbf{u}=\langle 3,3,3\rangle, \mathbf{v}=\langle 6,0,6\rangle,$ and $\mathbf{u}-\mathbf{v}$...
5 answers
In Exercises $25-40,$ use Descartes'rule of signs to obtain information regarding the roots of the equations.$$5 x^{4}+2 x-7=0$$
In Exercises $25-40,$ use Descartes'rule of signs to obtain information regarding the roots of the equations. $$5 x^{4}+2 x-7=0$$...
5 answers
In Problems $9-14,$ solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems $81-86 ext { of Section } 5.1 .]$Solve $f(x)<0,$ where $f(x)=x^{2}(x-3)$
In Problems $9-14,$ solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems $81-86 \text { of Section } 5.1 .]$ Solve $f(x)<0,$ where $f(x)=x^{2}(x-3)$...
5 answers
2) Which of the white blood cells shown below are present abnormal proportions? In your answer vou should hypothesise what disease/condition could account for these abnorma counts:3) Which of the white blood cells below appear to be have morphology that is different to what you have observed?oon
2) Which of the white blood cells shown below are present abnormal proportions? In your answer vou should hypothesise what disease/condition could account for these abnorma counts: 3) Which of the white blood cells below appear to be have morphology that is different to what you have observed? oon...
5 answers
(3) The density of air according to one source is 1.205 kglm? Convert this value to uglin: ., Show all work to receive credit: [3 pts]
(3) The density of air according to one source is 1.205 kglm? Convert this value to uglin: ., Show all work to receive credit: [3 pts]...
5 answers
Reactions of Amines & Amides+ HzoDissociationNHzHCIAcid-base reaction:OHAmidation:KOAmide Hydrolysis:
Reactions of Amines & Amides + Hzo Dissociation NHz HCI Acid-base reaction: OH Amidation: KO Amide Hydrolysis:...
5 answers
5) A specific drive through receives 3 customers every 30 minutes 0n average. (a) What is the expected value of customers for them in an hour?(b) What is the probability that they receive exactly 5 customers in the next 90 minutes?(c) What is the chance that they do not receive any customers in the next 60 minutes?(d) What is the probability that they receives exactly 5 customers in the next 30 minutes?
5) A specific drive through receives 3 customers every 30 minutes 0n average. (a) What is the expected value of customers for them in an hour? (b) What is the probability that they receive exactly 5 customers in the next 90 minutes? (c) What is the chance that they do not receive any customers in th...
5 answers
€ U I 18 1 372 8 ! ' 1 1 1 1 E3 3 8 [ | 1 72 3 U H 1 0 1 Ez } 1 12 8 1 1 1 1 1 1 1 F 2 3? 1 L 1 3 1 1 1 10 1 8
€ U I 18 1 372 8 ! ' 1 1 1 1 E3 3 8 [ | 1 72 3 U H 1 0 1 Ez } 1 12 8 1 1 1 1 1 1 1 F 2 3? 1 L 1 3 1 1 1 1 0 1 8...
5 answers
The lile distribution (life in years of continuous 4S) ol" hard disk drives for computer system follows the Weibull distribution with the following parameters:8=27 and 0 =S.5years:The manufacturer gives warranty for year What is the probability that disk drive will fail during the warranty period? Find the mean life and the median life ( Bso) for the disk drive By what time will 99' of the disk drives fail ? (That is find the B, life )
The lile distribution (life in years of continuous 4S) ol" hard disk drives for computer system follows the Weibull distribution with the following parameters: 8=27 and 0 =S.5years: The manufacturer gives warranty for year What is the probability that disk drive will fail during the warranty pe...

-- 0.023511--