20. The function f is continuous at x = 1. Vx + 3 -. - V3x + 1 for x 1 x - 1 If f(x) = k for x = 1 then k = 1 (A) 1 (B) , (C) -2 (D) None of these,

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives and fz = 44,…

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Q: = x2 - 4x + 1 with domain [0, 3] f has ---Select--- v at (x, y) = f has ---Select--- v at (x, y) = f…

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Q: Suppose f is continuous on an interval containing a critical point c and f 1c2 = 0. How do you…

A: The critical point of  f is x=c and f'c=0.

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: Suppose (1, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: As we know from the double differentiability test, When rt-s2>0 and r>0 then minima will…

Q: 6. If f is continuous and f(x)dx=4 , '3 | xf(x?)dx=

A: Explained below

Q: 20 10 If f is continuous and f(x) dx = 18, find f(2x) dx. %3D

A:

Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: 1. If f(x)=∫0 to x(t^3+6t^2+5)dt then f″(x)=

A: Topic = Derivative As per guidelines , at a time only one question can be answered out of different…

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A: Solution: Explanation of equation (7.117) in the book: Given y=fx    ......(1) Now, (in the book)…

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A: Partial derivative of f w.r.t a variable is the indicator of the sensitivity of f towards that…

Q: The function f has a continuous second derivative, and it satisfes f(2) = 5, f'(2) = 0 and f"(2) =…

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Q: Suppose (2, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: We need to choose correct option.

Q: 4. Choose and work either a) or b), NOT BOTH. (a) Show that the function f (x) = sin z for x €R is…

A: In the question given that we have to solve any one of them. Let us solve the first one.

Q: (-x + 1for x 1 h(x) h is continuous at x=1

A: A function is continuous at a point x=a if it satisfies all the three conditions. 1) Function must…

Q: 5. [ 4 ifx2 Show that f(x) = is not differentiable at x = 2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: a) Find the critical value(s) of f(x) = x + 2sin(x) on the interval 0sxs 27

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x – 1) + 2" – x has a critical number…

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Q: 1. Suppose that f : [0, 0) → R is continuous and f(x) # 0 for all x > 0. If we have (f(x))? = 2…

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Q: 7. Suppose that f: R R is differentiable at c and that f(c) = 0. Show that g(x):= |f(x)| is…

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Q: Зx2 — 1 if x 1 Determine c and d so that f is continuous everywhere

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Q: If we use Simpson's rule for a function f(x) = X +1 with n=4 , then the approximate of S f(x)dx is

A:

Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: Assume that f'(c) = 0 and that f'(x) changes from + to - at the critical point x = c. This means…

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Q: Locate and classify all the critical points of the function.(If an answer does not exist, enter…

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Q: Suppose (0, 2) is a critical point of a function with continuous second derivatives. In each case,…

A: The discriminant of a function, f at x,y is calculated using the formula: D=fxxfyy-fxy2 . If…

Q: 5. Ifc is a critical point of F(x), when the is a local maximum or minimum at c? Explain

A: To give the condition of local maximum or minimum at c if c is a critical point of F(x).

Q: Find the value of K that make the functionf continuous at x=2 パ-4 マー3x+2 sin(rx) + kx + k if x > 2…

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Q: If c is a critical point and the derivative of the continuous function f (x) doesn't change from…

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Q: 3. Show that x? if x>0 0 if x<0 f(x) = is differentiable at xo =0 but f' is not differentiable at xo…

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Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

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Q: 18 9. If f is continuous and f(x) dx = 14, find f(2x) dx. !!

A: Solution is in step 2

Q: b) Show that the function f (x) = { * x² sin ! for x E (0, 1] for x = 0 is absolutely continuous on…

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Q: 12. Consider x²y x4 + y? f(x, y) : for (x, y) # (0, 0) and zero otherwise. Is f continuous at (x, y)…

A: For the solution follow the next step.

Q: 6- if f(x) is a continuous function at x = 0, then a = 1- cos 4x x0 V16+ Vx -4 3.

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Q: 16 8. If f is continuous and f(x) dx = 18, find f(2x) dx. %3D

A: Given integral, ∫016f(x) dx =18

Q: 4 If the critical number of the function f(x) =x is x 0, then the function %D is decreasing on (0,0)

A: We can find the decreasing interval as below.

Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: Suppose f is continuous on an interval containing a critical point c and f"(c) = 0. How do you…

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Q: 1 dt, for x > 4. In(t) Let F(x) 4

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Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives. In each case,…

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Q: 3.) if f(x)= akw f(x) = x-1 and (X) X-1 What is the valule of

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Q: 5. Consider the function S 2r – 1, si x < 2 f(x) = 6-x, si x 2 2. The Limit x 2 f(x) is:

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Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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Q: *show work*

A: Given:A continuous function y = f (x) is known to be negative at x = 4 and positive at x = 9.

Q: The function if x 1 has critical points at... (Choose all that apply.) x = 0 x = -1 x = 3

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Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

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Q: Find the value of k that makes function continuous at z=4 |2z + 6 z> 4 5z – k z< 4 f(z) = ualuo…

A: Continuity.

Q: Determine unknown constants a and b for which g(x) is continuous at x=1. [5x - 2 x 1

A: