Suppose h is a function such that h(1) = -2, h'(1) = 2, h"(1) = 3, h(2) = 6, h'(2) = 5, h"(2) = 13, and h" is continuous everywhere. Evaluate h"(u) du.

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

A: fx=x32

Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFf(x) = Vx+2.

A:

Q: Find the derivative of the function by the limit process. f(x) = 1/(x − 1)

A: We use the limit definition of the derivative

Q: Suppose that a PDF for a continuous variable X is given by if 0 x)=3/4

A:

Q: Suppose that Xis a continuous unknown with -4< X< 4  having PDF denoted fsatisfying f ( x ) = c (…

A:

Q: Compute dy/dx using the limit definition of the first derivative for f(x) = 3x2

A: Given function is f(x)=3x2. we have to find the derivative using limit definition .

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: Suppose f(x) = df Find the derivative dx In(In(In(In(x)))). f' (x) :

A:

Q: Show that the function is continuous. (x) = 3x cos 3x

A: Show that the function is continuous. (x) = 3x cos 3x

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: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

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

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

A:

Q: If f(x) = - x² + 3x, which of the following will calculate the derivative of f(x) (- 2(x + h) + 3) -…

A: We can find the derivative of the given function using the definition of of the derivative given…

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

A: The given function is fx=-5x. Obtain the derivative as follows.

Q: Let f(x) = √x. Find the derivative of f(x) at x = 2 by using the definition of the derivative as a…

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Q: Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0<x<, then…

A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

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  (∞ , -∞).

A:

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

A: Here the given function The first derivative of function f(x) is defined by limit prosses as

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…

A:

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…

A:

Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFF (x) = Vx + 2.

A:

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

A:

Q: 5. Use the concept of limits to find derivative of f(z) = (2z + 1)3 at z = -i.

A: Given function is f(z)=2z+13 We have to find the derivative of the given function at z=-i.

Q: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

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)…

A:

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

A:

Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x)  To find:- Use limit Definition of a derivative to find f'(3)

Q: 3) Use the limit definition of the derivative to find f' (x) if f(x) = - %3D

A:

Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

A:

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

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Q: 1. Let f(x) = 2 %3D Use the limit definition of the derivative to compute f'(-1). X+3

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Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

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: find the derivative by the limit process. f(x)=14-x^2

A: Here we find the derivative by the limit process fx=14-x2

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

A:

Q: Find the equation of the tangent line of f(x)=2x^2-4x+1 at (2,1) using the limit definition of a…

A:

Q: It appears that f is not differentiable at a = 0. Moreover, the tangent line does not exist at this…

A: yes it is true.