10. Given the function h(x) a) h(3) b) h(9) h(9) – h(3) = 2x + 7, find d) h'(3) e) h(9) h- (9) – h¯'(3) c) f) 9 - 3 9 - 3

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A: Limit definition of derivative is f'(x)=limh→0f(x+h)-f(x)h

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Q: Q1 Prove that the derivative of (2x +1) 2 is 4 (2x + 1) by using first principle derivative.

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Q: - Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

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Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

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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: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

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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

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A: Given  f(x) = x8-5x4+5x3-1 We have to find the end behavior of the function.

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Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

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A: We have to check

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Q: B)Is w = Zez analytical function or not?

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Q: The derivative of f(z) - (+10z) is O6z (2z + 10) O6z (2z+10) O 6z (2z + 10) O 6z+60

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Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

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Q: Q1 Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

A: as per our guidelines we are supposed to answer only the first question. Kindly repost other…

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A: 1. We solve first order derivative of f(x)

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A: Given function, f(x)=x2-4x-5;x-5;x&lt;5x+1;x≥5; The objective is to tell whether the function is…

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Q: In(8z) Siven f(z) the derivative f'(x) is 8. %3D O 8 8x o 1 O 78z 1 8x 1/8

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Q: Find the derivative by the limit process. f(x) = 15 – x²

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Q: In(4z+10) Find the derivative of the function f(z) = z'sin(9z + 12) + %3|

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Q: [1, 2). over Calculate M6 for f(x) = 3 · In(x³) M6

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A: On solving this we will get

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Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: Compute the derivative of f(x) = (3x² – 1)1/4. %3D - O (6x – 1)!/4 a(322 – 1)5/4 O 3 2*(3x² – 1)-3,…

A: