let f(x)={x^2+2, x >-1 AND -x^2-x, x less than for equal to -1} compute f(0), f(-1)and f(-2) a. 0, 2, 6 b. 2, 0, 6 c. 2, 2, 6 d. 2, 0, -2 e. 0, 1, -2

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Q: Find f'(x). f(x) = O O O 6x - sin² (5x) f'(x) = O f'(x) = f'(x) = f'(x) = = 6-10sin(5x)cos(5x) 2√6x…

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

A: We  will compute the derivative of given function  by using first principle of derivative

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A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

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A: Given: f(x)=4x3+x+3, 0, 1

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Q: Verify Mean Value Theorem for the function f (x) = -6x+x³ over the interval [1,3]. %3D

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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x +1 on [-1,3]

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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

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Q: Verify Mean value theorem for the function f(x)=4x^3 over the interval  [0, 2].

A:

Q: 4. Differentiate the function. (1) f(x)= in x (2) f(x)= In{x (3) f(x)= In- 2x²(x+2)³ (3x- 2) (4)…

A: HI there, At a time we can answer only one question. So, I have answered first question.

Q: (b) Verify mean value theorem for f(x)=x² - 5x+6 over the interval [1,3].

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Q: Suppose that f(1) = -3, f(4) = -4, f'(1) = -3, f'(4) = -5, and f" is continuous. Find the value of…

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Q: Verify Mean Value Theorem for the function f (x) = -6x+x3 over the interval [1,3].

A: f(x)=-6x+x3

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Q: Verify Mean value theorem for the function f(x) = 4x° over the interval [0, 2].

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Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

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Q: Find four relations from {a,b} to {x,y} that are not functions from {a,b} to {x,y}.

A: Given: Let A=a, b and B=x, y To Find: Four relations from A to B that are not functions.

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A: