-2+h Evaluate the limit lim h

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: Give an example of two differentiable functions f(x) and g(x) such that: lim, 00 f(x) = lim, 0 9(x)…

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

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Q: For the function graphed here, show that

A: The given graph of the function is,

Q: The graph of the function f(x) = tan a is given above for the interval z e [0, 27] ONLY. Determine…

A: Given

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: 1 1 (b) lim x-0 'tan x e* – 1 -

A: =?

Q: Evaluate the limit using L'Hôpital's rule e – x I – 1 lim 5x2

A: See the details solution in below

Q: If a function f has no limit as x approaches c, then we say that lim f(x)

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Q: Find the limit by interpreting the expression as an appropriate derivative. e2x 1 lim- = i x→0 X

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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: 6. Use the graph of the function f(x) = He to discuss the limit lim 40 f (x). 1+e!/x

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Q: Evaluate the limit.

A: We have to evaluate the following limits- limh→0sin4h4h

Q: D-the result of the following limit is 1² lim x-0 In (sec x)

A: Let's evaluate given limit.

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: Consider the following. x² – 2 if x * 0 if x = 0 f(x) = y -2 -1 Use the graph to find the limit…

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Q: Suppose function f has the graph as shown below. Find the value of the indicated quantity if it…

A: We have to find the limit : limx→-0.5f(x) This will only exits if the left hand limit and right hand…

Q: For what value of the constant c is the function f continuous on (-o, 0)? cx2 + 3x if x < 2 f(x) =…

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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: Help me filling the blank spots. Thank you very much

A: We have to solve the problem

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: Let ƒ(x) = x^(1/(1-x)). a. Make tables of values of ƒ at values of x that approach c = 1 from above…

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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: Use the limit definition of the derivative f(x) – f(a) f'(a) = lim х — а to find f'(a) in each case.…

A: Consider the given function: fx=x3-7 Limit definition for derivative says: f'x=limx→afx-fax-a Find…

Q: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

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Q: Evaluate this limit for the given value of x and function f(x). limh->0 [f(x+h)-f(x)]/h f(x)=…

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Q: se x+0 has a limit on the point X = 0. Show if the function f(x) = (o, se x = 0

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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: Please show step-by-step solutions

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Q: Let f(x) = 2л-5х' Then the slope of the tangent line to the graph of y = f(x) at the point (T, -) %|…

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Q: If f(x)f(x) is a function, explain what we mean by the derivative f′(x)f′(x). Answer A and B below:…

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Q: Guess the value of the limit (if it exists) by evaluatingthe function at the given numbers (correct…

A: To determine: The value of the limit (if it exists) by evaluating the function at the given numbers…

Q: Suppose function f has the graph as shown below. Find the value of the indicated quantity if it…

A: The limit of the function is the value of the function such that when its parameter approaches a…

Q: 7. Explain why for any function g, limg(c +h) = lim g(x). Use this to show that f'(c) = lim f(x) –…

A: Consider the given function limh→0gc+h=limx→cgx

Q: Let -2x² + 6x - 3 for x 0. According to the alternate form of the definition of the derivative, to…

A: We will use properties derivative.

Q: 4x – 7a? for x 0 . f(x) According to the definition of the derivative, to compute f' (0), we need…

A: Please see the explanation below

Q: (2 + h)? - 4 lim h→0 h

A: Given limh→0(2+h)2-4h

Q: Use a table of values to estimate the value of the limit. If you have a graphing device, use it to…

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Q: find the limit or explain why it does not exist

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Q: S -2x? + 5x 7x² – 5 for x 0. According to the alternate form of the definition of the derivative,…

A: Given:

Q: 3 of the If f(x) = , find f'(3), using the definition of derivative. f'(3) is the limit as x →…

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Q: lim, x – 1 x→-∞ p² +1 - -00

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Q: х, x 1

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Q: Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct…

A: The given limit is limx→-3x2-3xx2-9

Q: Find the value of the limit lim 01 0 0 O DNE x3 x+0 x³ + x2 < Previous

A: On solving this we will get

Q: Find the limit by interpreting the expression as an appropriate derivative. e2x lim- 1 i X0

A: As we already know that, dydxx=a=limh→0f(a+h)-f(a)h

Q: -5x? + 2x for æ 0 According to the definition of derivative, to compute f'(0), we need to compute…

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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: Consider your answers from the previous problem for the piecewise function x > -4 f(x) = X+4…

A: Check the function limit is exist or not and check the function continuity