V16 + h – 4 lim

Q: The limit below represents a derivative f'(a). Find f(x) and a. (2 + h)* – 16 - lim h→0 h f(x) = ...…

A: Compare the given expression with the formula of first derivative to write the function and the…

Q: Find the limit by evaluating the derivative of a suitable function at an appropriate point. Hint:…

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Q: Identify this limit as derivative; Lim it's f'cx) whe'e fa)E - メ+Ax 7.

A: We need to find limit as f'(x)

Q: Use the limit definition to find the derivative of the function. f(x) = 2x + 4 f(x + h) – f(x)…

A: Given, Function, f(x)=2x+4

Q: Suppose f(x) can find a derivative at x = a, then the following limit is equal to f'(a) is ( ).…

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Q: Use the following definition of a derivative fla=lim f\x-f(a) x-- a x-a To find fa), where f x=x°-…

A: Given, f(x)=x3-2x  To find f'(a).  Solution: f'(a)=limx→af(x)-f(a)x-a      =f(a)-f(a)a-a=00

Q: The limit represents a derivative f' (a). Determine f(x) and a. 12h lim h 1 h→0 (Express numbers in…

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Q: The limit below represents a derivative f' (a). Find f(x) and a. 43+h - 64 lim h-0 h f(x) = a =

A: The limit below represents a derivative f'(a) defined byf'(a) = limh→0 43+h-64h  ....(1)we find f(x)…

Q: Use the limit definition of the derivative function to find 4 x2|. Which of the following is the…

A: We need to evaluate the correct step that comes just before using the direct substitution to…

Q: find limit that represents the slope of the tangent line to the following function at x = 2 ? 2 f(x)…

A: Given function f(x)=24-3x To Find that represents the slope of the tangent line to the following at…

Q: f′(x). Find the doma

A: Derivative and function: Derivative by limit definition-h→0limf(x+h)-f(x)hf(x)=2-7xf(x+h)=2-7(x+h)

Q: Use the function below to answer parts (a)-(c). f(x) = x? + 1 (a) Use the formal definition to find…

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Q: For Exercise evaluate each limit by first converting each toa derivative at a particular x-value.

A: limx→-1x29-1x+1 On simplification, we get limx→-1x29-1x+1=limx→-1x29--129x--1 Now it is in the form…

Q: The limit below represents a derivative f'(a). Find f(x) and a. (6 + h)ª – 1296 lim h>0 h f(æ) = %3D…

A: Given that,  f'(a)=limh→0(6+h)4-1296h we have to find the value of f(x) and a.

Q: Using the definition of the derivative, find f'(x). Then find f'(-3), f'(0), and f'(4) when the…

A: f(x)=2x3+10

Q: Use the definition f' (c) = lim,0 f(c+h)-f(c) to find the derivative. h f' (2) if ƒ (x) = 3 x+2 O…

A: Given that, f(x)=3x+2 We have to find f'(2)   As we know, f'(c)=limh→0f(c+h)-f(c)h   ......(1)

Q: The limit below represents the derivative of some function f(z) at some number a. 6(3+ h) - 162 lim…

A: Definition: The derivative of function fx at a point x=a is given by limh→0 fa+h-fah.

Q: The given limit represents the derivative of a function f at some number c. Determine c andf for the…

A: derivative by limit is given as f'(x) = limh→0 f(x+h)-f(x)hat x = cf'(x) = limh→0 f(c+h)-f(c)h

Q: b. Determine if the lim f(x) exists, if f(x) is defined as follows: X4 12x + 3, 5x-9, x < 4 x 24…

A: Both question are solved as, follow

Q: Use the definition of the derivative to evaluate the following limits.

A: Derivative of a function f(x) is defined as, f'(x)=limh→0f(x+h)-f(x)h. Derivative of a function f(x)…

Q: The limit below represents a derivative f '(a). Findf(x) and a. (5+ h)? - 25 lim h-0 f(x) = a =

A: Given: f'a=limh→05+h2-25h We know that, f'x=fx+h-fxh On comparing both expression, we get fa+h=5+h2…

Q: The limit below represents a derivative f' (a). Find f(x) and a. (3+ h)² – 9 lim h→0 h f(x) = a =

A: Given limh→03+h2-9h

Q: Which of the following is the correct limit defihition for the derivative of g(x) = + 4? Select the…

A: Consider the formula for the limit of the  function f(x).

Q: f(x) = { S -4x? + 4x for x 0. According to the definition of the derivative, to compute f'(0), we…

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Q: Let 1 f(x) = x +3 Use the limit definition of the derivative to find the following. (a) f'(-7) = (b)…

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Q: Each limit represents a derivative f '(a). Find f(x) and a.

A: Since, we have been given that f'(a)=limx→5x3-125x-5⇒f'(a)=limx→5x3-(5)3x-5-(i)

Q: Find the value of the limit below. [2 - 5(x + Ax)]? - (2 – 5x)? lim Ax0 Ax Specify the function f…

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Q: The limit below represents a derivative f'(a). Find f(x) and a. (2+ h)* – 16 lim h-0 h f(x) = %3D a…

A: We have to find the function f(x) and value of a from the given limit.

Q: Given f(x) = 3√x, find f'(x) using the limit definition of the derivative, f(x +h)-f(x) f'(x) = lim…

A: Given the expression for the derivative of the function is: f'x=limh→0fx+h-fxh And fx=3x

Q: (8+h)³ – 512 lim h-0 h

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Q: Given the function f(x) = 5 ln(x – 1), write an expression that represents the derivative of f using…

A: Given function, f(x)=5lnx-1

Q: The limit V4+h-2 lim h0 h represents the derivative of some function f(x) at some number a. Find f…

A: Solved below

Q: Use the given graph of the function f(x) to estimate the limit lim f(x) I→-7 (Use infinity, negative…

A: Your graph

Q: The limit below represents a derivative f'(a). Find f(x) and a. (3 + h)* – 81 lim h→0 h f(x) = a =

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Q: The limit below represents a derivative f' (a). Find f(x) and a. (5 + h)? – 25 lim h-0 h f(x) a =

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Q: The given limit represents the derivative of a function y = Rx) at x= a. Find (x) and a. lim (8(7 +…

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Q: The limit below represents a derivative f'(a). Find f(x) and a. (6 + h)? – 36 lim h→0 h f(x) = a =

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Q: Given f(x) = 2 /x + 2, find f'(x) using the limit definition of the derivative. f'(x)=

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Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: m = f'(x)

Q: Given f(x) = 3 – 4x°, find f'(x) using the limit definition of the derivative. f'(x)=

A:

Q: (2 + h)? - 4 lim h→0 h

A: Given limh→0(2+h)2-4h

Q: Given the function f(x) = 4x³, determine the derivative of f at æ = –2 using the limit shown below.…

A: We will find the required limit which will be used to find derivative at x=-2 as following.

Q: Based on the given values, is the function continuous or not? If not, select the condition which is…

A: A function is said to be continuous at x=c if limit of function at x=c exists that is limx→cf(x)…

Q: Given f(x) = 4 – 3x, find f'(x) using the limit - definition of the derivative. f'(x)=

A: The given function is:fx=4-3x2To find f'x

Q: If f(x) = v4+4x, find f' (4), using the definition of derivative. f' (4) is the limit as x → of the…

A: By the definiton of limit to find f'(4) the limit of x goes to 4 and we find the limit of the…

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: The given function is, f(x)=3x+9. Obtain the value of the limit.…

Q: The limit below represents a derivative f (a). Find f(x) and a. (6 + h)° – 216 lim h→0 h f(x) = a =

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Q: Find the value of the limit below. [9 - 4(x + Ax)]? – (9 – 4x)2 lim Ax - 0 Ax Specify the function f…

A: We have to find given limit.

Q: Given f(x) = 4/x – 5, find f'(æ) using the limit definition of the derivative. f'(x)=

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Q: Use the limit definition to find the derivative of the function. f(x) = 3x + 5 f(x + h) – f(x)…

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