Compute the derivative of f(x) = x³/2 using the limit definition. Hint: Show that f(x + h) – f(x) _ (x +h)³ – x3 1 - h V(x +h)3 + Vx³

Q: 6.) Use the limit definition of the derivative to find f' (x), given f(x)=x-3 x+5

A: Consider the function

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. f(x) = x2 - 2 %3D f'(x) = 2x %3D Need…

A: Apply Limit rule

Q: 2. Let f (x) = x² + 3x – 5. а. Use the formal limit definition of the derivative to compute f'(x).

A: Given,          fx=x2+3x-5

Q: Use the limit definition of the derivative to compute f'(x) for f(x)= 1/ sqrt of x

A: Given, f(x)=1x

Q: Q4: Use the limit definition to compute the derivative, f(x), for 1.F(x) = xi 2.F(x) = V - r

A:

Q: Find the derivative of g(x)= using the limit definition

A: Solution:we have use formula…

Q: Let f(x) = 2x² + 1. Use the limit definition of the derivative to find f'(x).

A:

Q: Let f (x) = x² – 4. a. Find f'(x) using the formal limit definition of derivative. -

A: The formula of formal limit definition of derivative is  : lim h →0  [{f(x+h) - f(x)} / h ]

Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 7.

A:

Q: Compute the derivative of f (x) = x3/2 using the limit definition. Hint: Show that

A: we have;  f(x)=x32

Q: Q4: Use the limit definition to compute the derivative, f(x), for 2.F(x) = Vx³ – x

A:

Q: Let f(x) = 2x2 + x. Determine f'(1) using the definition of the derivative as a limit.

A:

Q: Let f(x) = 1/x-2. Find f'(x) using the limit definition of the derivative

A: We find f(x+h) first.

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: Compute the derivative of f (x) = x 1/3 using the limit definition.                            (x +…

A: Given: fx=x13 To Find: The derivative of the given function using limit definition

Q: (a) Let f (x) = Vx – 1. Use the limit definition of the derivative to find f' (x).

A:

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

A:

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: n(x)=3x?4k+1 %3D

A:

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

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Q: ) Use the limit definition of derivative to compute k'(x).

A:

Q: Q4: Use the limit definition to compute the derivative, f(x), for 1.F(x) = x3 2.F(x) = = Vx3 - x

A:

Q: Let f (x) = 2x² + 1. Use the limit definition of the derivative to find f'(x) %3D

A:

Q: Find f'(x) using the limit definition of derivative.

A: We have given,

Q: Compute f'(3) using the limit definition of derivative if f

A: Given: f(x)=6x2f'(3)

Q: Let f(x)=x2-5x. Use the limit definition of the derivative to find f' (1)  Use the limit definition…

A: We have to find f'1 by limit definition of the derivative for the given function: fx=x2-5x We know…

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

A: Explanation of the answer is as follows

Q: .. Consider the quadratic function y = 4-x². Using the limit definition, ind the derivative of the…

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: let f(x)= 5x2. Show that f(3+h)=5h2+30h+45. Then show that  (f(3+h)-f(3))/h=5h+30 and compute the…

A: Compute: f(3+h)

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 first derivatives test to find the local exterma of f(x) =x3-12x on R

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Q: Use the limit definition of the derivative to prove the following special case of the Product Rule:…

A:

Q: Find the derivative of the given function using the limit definition f(x) = ;1 = %3D

A:

Q: 3. Use the limit definition of a derivative to find f'(x) if f(x) = 3x2 - 5x %3D

A: f(x)=3x2-5x

Q: Let f(x) = V5x + 2. Find the derivative f'(x) using the limit definition.

A: We have to find derivative

Q: Find the derivative of the following functions using the limit definition. 1. y = x² – 4x – 5 -

A:

Q: Find the derivative of the following function using the limit definition: z =7y2- 11/x

A: We need to find derivative.

Q: Use the limit definition of derivative to find r at the point c= 2.

A: The given function is fx=x5 ...(1). By using the limit definition of the derivative, the derivative…

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

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Q: II) By using the limit definition of derivative, prove the identity J dzf(2)8' (2) = - / da f…

A:

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

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Q: Let f(x) = 2x2 +1. Use the limit definition of the derivative to find f'(x).

A: We can find f'(x) Using following formula

Q: Compute the derivative of f(x) - directly from its definition as the limit of a difference quotient.

A:

Q: Given g(x) ニ X-1

A: We know that, g'(x)=limh→0g(x+h)-g(x)hHere g(x)=1x-1Therefore…

Q: 1 . Let f(r) 2r + 1

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Q: Q4: Use the limit definition to compute the derivative, f'(x), for 2 1.F(x) = x3 2.F(x) = Vx³ – x

A: