5

Give an example where Theorem 6-18 is not true if f (x) is not continuous...

Question

Give an example where Theorem 6-18 is not true if f (x) is not continuous

Give an example where Theorem 6-18 is not true if f (x) is not continuous



Answers

Give an example of: A continuous function $f$ on the interval [-1,1] that does not satisfy the conclusion of the Mean Value Theorem.

True or false. If a function is not differentiable, then it is not continuous. So a function is not differentiable at a point If that point is not continuous or if there is a sharp corner at that point, or if the tangent line of that point is vertical. Yeah, the statement is false. A function that's not differentiable may have a sharp corner but be continuous or have a vertical tangent line, but be continuous. An example of such a function is F. Fx equals the absolute value of X. So the graph of this function looks something like this. This function is not differentiable right here at this point X equals zero, but it is continuous there, so this is their final answer.

Hello. There it is exercise. We need to give an example of the function that is not differentiable at origin. So let's consider the following function. It was to the square it of X squared plus y square. You can observe that if we take the partial derivative of this function with respect to X. We obtain here X divided by the square root of X square plus Y squared. And similarly if we take the parts of there, but with respect to why there's just why divided the square root of X squared plus Y squared. Both of these partial derivatives is um have is not continues at +00. So that means that this function is not differentiable at the point 00 or the origin. It specifying this exercise and it happens that this corresponds to a cone and the tip is not differentiable always. When you consider some cone, the tip is not differentiable. And then basically if you want to function that there's no differential at some specific point you need to give some example. Well you can choose equation of a cone and you locate the tip at that point. Okay?

True or false. There's a function which is continuous on the closed interval from negative 1 to 5 but not differentiable at the point X equals three. So this point x equals three will be continuous because it's within this interval that were given but it will not be differentiable. Therefore there should be a sharp corner or a section that is vertical so that the tangent line will be vertical. Mhm. These are our two options for a point that is continuous but not differentiable. An example of a graph that's continuous everywhere but not differentiable at one is the graph of the absolute value of X. So this graph looks something like this. So this for text right here at X equals zero is the only non differentiable point. We can translate this graph along the X axis and put this vertex wherever we want there to be a non differentiable point. So if we wanted there to be a non differentiable point at a for example, so the graph would look like this, we would have, instead of the absolute value of X, we have the absolute value of x minus A. So in this case we want a function that is not differentiable at the point X equals three. So our function would be f of x equals the absolute value of X -3. Yeah. And if we graph that, yeah, Where here is one, here is three, Here is five, this is approximately what our graph looks like and you can see this function is continuous over the interval from 1 to 5 and it is not differential at this point, X equals three. So this statement is true And the function f of x equals the absolute value of X -3 is an example that illustrates this statement.

True or false. If a function is differentiable than it is continuous, we know that the derivative of a function at a point is the slope of the tangent line at that point, and a function cannot have a tangent line at a point that doesn't exist. Mhm or is otherwise discontinuous. Mhm. So this statement is true, and an example of a function that is differentiable and continuous everywhere is F of X equals X squared plus two. This is our final answer.


Similar Solved Questions

5 answers
Point)Calculate the Total Flux of the field F(x, Y, 2) = (3x 2y - S)i + (3y + 2x 8)j + zk outward through the surface of the closed cylinder x2 + y2 < 4 and -9 < 2 < 9.The Total Flux is the flux across the top and sides and bottom where: 1. Flux across the top2. Flux across the sidesFlux across the bottom
point) Calculate the Total Flux of the field F(x, Y, 2) = (3x 2y - S)i + (3y + 2x 8)j + zk outward through the surface of the closed cylinder x2 + y2 < 4 and -9 < 2 < 9. The Total Flux is the flux across the top and sides and bottom where: 1. Flux across the top 2. Flux across the sides Flu...
5 answers
Ezz 417 |z2 | +uetu (OzU 1z| €z wn +zU K(I+u) aoe U (I+( '+Ulacu Le2 Wun 1+ Wii _ t+uc (O0=T+zu ",(T-)IOJ 9u981OAU0D JO 819 JUO pue Sn{peI 94} pUL (squrod OT) (t) 'Squtod 08 jo
Ezz 417 |z2 | +uetu (OzU 1z| €z wn +zU K(I+u) aoe U (I+( '+Ulacu Le2 Wun 1+ Wii _ t+uc (O 0= T+zu ",(T-) IOJ 9u981OAU0D JO 819 JUO pue Sn{peI 94} pUL (squrod OT) (t) 'Squtod 08 jo...
5 answers
4. Solve +7z =-1 the j8 4 NOT FORGET 2
4. Solve +7z =-1 the j8 4 NOT FORGET 2...
5 answers
You are moving and need a rental truck The rental company you have chosen charges S70day (e8 plus SO 20 for every mile you Iravel Write linear equation ihat exprosses Ina Iotal costy where * reprasents the number of miles you Iravol, Graph Ihis equation Then choose nurber ol mlles, YOu travel that day and find tho tolal cost of renting Ihe Iruck
You are moving and need a rental truck The rental company you have chosen charges S70day (e8 plus SO 20 for every mile you Iravel Write linear equation ihat exprosses Ina Iotal costy where * reprasents the number of miles you Iravol, Graph Ihis equation Then choose nurber ol mlles, YOu travel that d...
5 answers
Suppose the position ol an obeci movngstraighl line given by s() = 21Fird the instanlaneous velocity at time [=2The inslantaneous velocity at (=2 I5
Suppose the position ol an obeci movng straighl line given by s() = 21 Fird the instanlaneous velocity at time [=2 The inslantaneous velocity at (=2 I5...
5 answers
Point) The region W the cone shown below:angle at the vertex is T/ 2, and the top dlat and at a height of 1.Wirite the limits of integration for Jw dV the following coordinates do not reduce the domain integration by taking advantage of symmetry}:Cartesian: WithandVolume(b) Cylindrical: WVithandVolume J jd $(c) Spherical: WithVolume
point) The region W the cone shown below: angle at the vertex is T/ 2, and the top dlat and at a height of 1. Wirite the limits of integration for Jw dV the following coordinates do not reduce the domain integration by taking advantage of symmetry}: Cartesian: With and Volume (b) Cylindrical: WVith ...
5 answers
The average coefficient of volume expansion for carbontetrachloride is 5.81 ✕ 10−4 (°C)−1. If a46.5-gal steel container is filled completely with carbontetrachloride when the temperature is 10.0°C, how much will spillover when the temperature rises to 28.5°C? (Assume the coefficientof thermal expansion of steel is 11 ✕ 10−6(°C)−1.)
The average coefficient of volume expansion for carbon tetrachloride is 5.81 ✕ 10−4 (°C)−1. If a 46.5-gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0°C, how much will spill over when the temperature rises to 28.5°C? (Assume t...
5 answers
What is the freezing point of a solution that contains 20.0 g ofglucose (C6H12O6) in 100.0 g ofH2O? Kf for water is1.86°C/m.A) -1.86CB) -2.06CC)+1.11CD)+0.111CE)-0.206C
What is the freezing point of a solution that contains 20.0 g of glucose (C6H12O6) in 100.0 g of H2O? Kf for water is 1.86°C/m. A) -1.86C B) -2.06C C)+1.11C D)+0.111C E)-0.206C...
5 answers
C) fkx)=X+1/x- 1Domain: {x e RIx#1} Range: {y e Rly#1} Restriction: X # 1,Y#1 Intervals of increasing: noneIntervals of decreasing: always decrease Roots: X=-1 Y intercepts: ( 0,-1 ) Vertices: none
c) fkx)=X+1/x- 1 Domain: {x e RIx#1} Range: {y e Rly#1} Restriction: X # 1,Y#1 Intervals of increasing: none Intervals of decreasing: always decrease Roots: X=-1 Y intercepts: ( 0,-1 ) Vertices: none...
3 answers
Let2 dWFind a,b,c,d,e,f,g so that (u, V, w)is orthonormal:
Let 2 d W Find a,b,c,d,e,f,g so that (u, V, w) is orthonormal:...
4 answers
Mangje lue Dollowng mokrule sin ordet ol decreasing Iatlice energy? U,sc WodiMaaNacl Sic MgCz> UFMgClz Lif > Naa SicSic Mgdz LF > NaClLif Na SiC > MgClz
Mangje lue Dollowng mokrule sin ordet ol decreasing Iatlice energy? U,sc WodiMaa Nacl Sic MgCz> UF MgClz Lif > Naa Sic Sic Mgdz LF > NaCl Lif Na SiC > MgClz...
5 answers
Lajetmine Ihe Iargest interval (a b) Ior which Thoorem puuantee- 2ut+ 31Y"" - Zxy" -y-0 V-#-(-A)-r(-9)-Julype25 Voug ansmul ntetal nolaton |
Lajetmine Ihe Iargest interval (a b) Ior which Thoorem puuantee- 2ut+ 31Y"" - Zxy" -y-0 V-#-(-A)-r(-9)- Julype25 Voug ansmul ntetal nolaton |...
5 answers
4. Least Squares Linear Predictor Suppose that X is normal (Ux, 0}), Y is normal (uy, 6}) , and the two random variables are independent: Let S = X+Y. a) Find the conditional distribution of X given $ =b) Find the least squares predictor of X based on S and provide its mean squared error:c) Find the least squares linear predictor of X based on S and provide its mean squared error:
4. Least Squares Linear Predictor Suppose that X is normal (Ux, 0}), Y is normal (uy, 6}) , and the two random variables are independent: Let S = X+Y. a) Find the conditional distribution of X given $ = b) Find the least squares predictor of X based on S and provide its mean squared error: c) Find t...
3 answers
I < 0), where T(a) Jo tr-Ie-'dt is the Gamma(1, gatretrea funection 8) (Hence , Exp(8) .) Let Camma when Gamma(%, B) be independentp and lelez X X+Ca; (a,8) and formula to prove that Use the 2 Gamma(a convolution facts that + 7,8). [Note: Tla + 1) = aT(a) for & € R You may use the and T(n) = (n - 1)! for n €N J6 t-'(I ~ t)"-idt=2t-'I()I6) /T6+5) for T,s,1! foj and
I < 0), where T(a) Jo tr-Ie-'dt is the Gamma(1, gatretrea funection 8) (Hence , Exp(8) .) Let Camma when Gamma(%, B) be independentp and lelez X X+Ca; (a,8) and formula to prove that Use the 2 Gamma(a convolution facts that + 7,8). [Note: Tla + 1) = aT(a) for & € R You may use the ...
5 answers
Note: For all hypothesis test; elearly state the following: the null and alternate hypotheses; and the level of significance; b)ihe critical value and rejection regions; c) the value of the test statistic; d) the p-value; your decision; and interpret your decision cuntext.
Note: For all hypothesis test; elearly state the following: the null and alternate hypotheses; and the level of significance; b)ihe critical value and rejection regions; c) the value of the test statistic; d) the p-value; your decision; and interpret your decision cuntext....
5 answers
F] 4oooanGonDtecrInvabauuqh zOlxb F = d4 (Dporvz 2 (hp+ Wp1ai @ov€ Gwmoloj ayt uQf 367 po 1o onion 24f apomio) {bJa EE Jentpo) to WnS Tnox m0xb at ?idwpx3 (4+T-U to 5[u324430) purs _ ur 03141+ V ( {8o [n (Lu) N= *x Pf8 4p Sonrojd Fonion Vex0 = /5 6 1
F] 4oooan Gon Dtecr Invabauuqh zOlxb F = d4 (Dporvz 2 (hp+ Wp1ai @ov€ Gwmoloj ayt uQf 367 po 1o onion 24f apomio) {bJa EE Jentpo) to WnS Tnox m0xb at ?idwpx3 (4+T-U to 5[u324430) purs _ ur 03141+ V ( {8o [n (Lu) N= *x Pf8 4p Sonrojd Fonion Vex 0 = / 5 6 1...
5 answers
Which of the following compounds matches the 1H NMR spectrum shown below?Saveman0 PrTA. isopentyl acetateaqueous sodium bicarbonateC. isopentyl alcoholD. acetic acid
Which of the following compounds matches the 1H NMR spectrum shown below? Save man 0 PrT A. isopentyl acetate aqueous sodium bicarbonate C. isopentyl alcohol D. acetic acid...

-- 0.022106--