Suppose h is a function such that h(2) = -2, h'(2) = 2, h"(2) = 4, h(5) = 5, h'(5) = 7, h"(5) = 12, and h" is continuous everywhere. Evaluate h"(u) du.

Q: Find the derivative of the function by the limit process. f(x)= 2/x2

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Q: Compute the derivative of f (x) = x 3/2 using the limit definition.

A: fx=x32

Q: Find the derivative of the function by the limit process. 9. f(x) = %3D f'(x) =

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Q: 5. Use the limit definition of derivative to find f'(x) if f(x) = VT.

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Q: Find the derivative of the function by the limit process.

A: Given: fx=x2+x-3 To Find: The derivative of the given function by the limit process

Q: Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2,…

A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…

Q: The following figure gives the graph of the derivative of a continuousfunction ƒ that passes through…

A: The graph limit of the derivative of a continuous function is -3≤x≤1. The limit of variable x at y=0…

Q: Find the derivative by the limit process. f(x) = 11 – x2

A: We have to find the derivative by the limit process where f(x) = 11 – x2.

Q: FIND THE DERIVATIVE BY THE LIMIT PROČESS OFF(x) = Vx+2.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: Find the derivative of the function by the limit process.

A: Consider the given function fx=1x2   Derivative of any function fx using limit process is…

Q: п-(х-4)" 22и. (2n — 1) Ax) =En=0 n:

A: Solution of given problem as follow

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: Find the derivative of f (x) = 2/x using the limit definition.

A:

Q: ) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x). %3D (3 Marks)

A: Answer - definition of derivative f'(x) = lim h tends to 0 ( f(x+h) -f(x) ) /h

Q: Give an example of a function that is continuous on -∞ < x < o but is not differentiable at x = 3.

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Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: Find the derivative by the limit process. f(x) = 14-x²

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Q: Find the derivative of the function by the limit process. f(x) = 5x − 4

A: fx=5x-4

Q: Give an example of a differentiable function ƒ whose first derivative is zero at some point c even…

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Q: 2. Shows that the function f(x)- x2-9 is continuous at x = 0, but has removable x-3 discontinuity at…

A: This question is taken from the limit in which we have to check the continuity at x=0 of the given…

Q: Show that the function is continuous on  (∞ , -∞).

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Q: Find the derivative of the function by the limit process. f(x) - f'(x) =

A: The given function is f(x)=4x2We have to find the derivative of f(x).

Q: Suppose f is differentiable with continuous derivative on [a, b]. Show that lim f(x) sin(nx) dr = 0.

A: To prove the given limit

Q: Give a justified example of function f(x) that is differentiable everywhere, yet its derivative has…

A: Definition of Differentiability p(x) is said to be differentiable at the point x = b if the…

Q: Suppose /has a continuous derivative on the interval [0, 6]. Assume also that f' is increasing on…

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Q: Find y' if y = 5x + 2 using the limit definition of derivative.

A: Given that  y=5x+2

Q: Find the derivative of f(x) = x In(x) 1- In(x) O In(x) O1+ In(x) O In(x) /x

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Q: 10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not…

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Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

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Q: Prove that if the function f : I → R has a bounded derivative on I, then f is uniformly continuous…

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Q: Find the derivative of the function by the limit process. f(x) = vX +7

A: Given,          The function is fx=x+7.

Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 3

A:

Q: 2. Use the definition = f'(x) = limw-x- S(w)-r(x). to find the derivative of w-x y = tan x.

A:

Q: Use the limit definition of derivative to find the slop of the tangent line of f(x)=5x^3+x at (1,6).

A: The derivative of the function is defined by,

Q: Suppose the second derivative of a function f is f" (z) 0 (-∞, 1) U (1, 3) U (5,00) ○ (3,5) O (1,3)…

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Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: Find the derivative of the function by the limit process. f(x)=x2+x-1

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Q: Compute the derivative of f(1) = In(x In(x² In(r³))).

A: The given function f(x)=lnx lnx2 lnx3

Q: Find the derivative by the limit process. f(x) = 15 – x²

A: Givenf(x)=15-x2Step -1From the definition of derivativef'(x)=lim∆x→0f(x+∆x)-f(x)∆x

Q: Let ƒ be a function that is continuous on [0, 2] and đifferentiable on (0, 2). Suppose that f (0) <…

A: Yes, we will show that f' necessarily take on both positive and negative values on (0, 2). If the…

Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: find the derivative of f(x)=x/(x+2) using the limit definition of a derivative

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Q: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

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Q: Would it be possible for a function to be continuous on [0,2) but not on [0,2]?

A: Let us consider the function f(x) =(x+4)/(x-2) .

Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: 1 Use the limit definition of the derivative to find f'(x) if f (x)= 10x

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Q: Find the derivative of the function by the limit process. f(x) = x3 - 9x + 1 f'(x)

A: We know,f'(x) = limh→0 f(x+h) - f(x)h  by limit processHere,f(x) = x3 - 9x + 1So,f(x+h) = (x+h)3 -…