We know that if f is differentiable, we can write the derivative function as f(x +h) – f(x) f'(x) = lim h→0 h f (x + h) – 2f(x) + f(x – h) h2 pothesize what lim t your hypothesis is correct. For example, you could compute the above limit for several f and show that the answer agrees with your hypothesis. should represent. Try to convince the h→0 (A small portion of your grade will be based on the correctness of your hypothesis, but you do show that vour hypothesis is correct.)

Q: 28. Find the derivative f'(x) for each of the following function. (1) f(x)=(2x-1)² (2) f(x)=e¹+x-lnx

A: To find the derivative f'x for each of the following function.1 fx=2x-122 fx=ex+x-ln x

Q: For the function given by q (x)= x² + 2x+1, use the limit definition of the derivative to compute…

A: Definition of the Derivative:        The derivative of f(x)  with respect to x is the function f'(x)…

Q: Explain what is incorrect with the following limit definition answers, and correct the errors. There…

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Q: 9. If f(x) 9x2 - x3, find f'(1) and use it to find an equation of the tangent line to the curve y 9x…

A: Compute the derivative of the function and find the derivative value at x=1.

Q: (Pls don’t use the L-hospital rule) Need help with this problem step by step. Thanks

A: Answer and explanation is given below..

Q: Let j(x) 1 Calculate j' (3). %3D 8 x+2 Answer): j' (3) =|

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Q: Find the derivative of the function by the limit process. f(x) = x² + x - 5 f'(x) =| 4x – 8

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Q: Please answer the question and show the solution (do note that there are two parts to the question).

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Q: Use the limit of the difference quotient definition to find the derivative, f'(x) must show the…

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Q: 45-46 Use the definition of a derivative to find/"(x) and f"(x). Then graph /. /", and /" on a…

A: We will use definition of derivative to find f'(x) . Then, again use definition of derivative on…

Q: Use the definition of a Derivative to show that the function is not differentiable at x = 1. Why is…

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Q: 6. The definition of the first derivative is f(x+h)+f(x) E. f'(x) = F. f'(x) h f(x+h)-f(x) h…

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Q: Please answer it neatly

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

Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x)…

A: Here ,               We have given a function now we have to solve it by using definition of limit…

Q: If limit t y = f(x) write an expression for the differentia dy

A: Given: y=f(x)

Q: Let f (x) = x2 + 1. Use two definitions of derivatives to find f'(1). %3D [Hint: The two definitions…

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Q: Question 1 Use the limit definition to find the derivative of f (x) = 3x - 2x² at x = 3. Then…

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Q: Let f(x) = 1- 5x2. Use the limit definition of the derivative to show tl f'(x) = –10x

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Q: f(x +h) – f(æ) Use the definition of a derivative f'(x) = lim to show if f' (0)does exist or h→0 h…

A: Given function is : fx=x2sin4x  , x≠00                 , x=0 Squeeze theorem: If xn≤yn≤zn for all…

Q: Concept Quiz: Finding Derivative of Function Using Definition of Derivative In this assignment, you…

A: The given function is  f(x) = 3x2 - 4x + 1 Now to find the derivative by using definition.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: