Use the Integral Comparison Test to show that dx diverges by comparing with the integral Vr +1 1 dx; make sure that you show that the functions satisfy the necessary inequalities to apply the 1 comparison test. 2+e¬* Use the Integral Comparison Test to determine whether or not dx is convergent or divergent-

Q: Let F(x) = f(xf (x²)). Suppose that ƒ(4) = 6, ƒ'(4) = 1, and ƒ'(12) = 5. Find F'(2).

A: Given, .Given,  f(4)=6, f'(4)=1 and f'(12)=5.

Q: Let f = e^ (− x ^3/ 3) +x−y^ 2 . Find the local minima, maxima and saddle points.

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Q: Given f(x) = x^3-3x^2 – 1. Use the first or second derivative tests to c) Determine the intervals…

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Q: 6 Y = x6 + Vx5 ++5 x3 y' = 6x5 +x² – 18x* y' = 6x5 +x1.5 – 18x-2 O Option 2 Option 1 y' = 6x5 +x15 –…

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Q: ind the relative (local) maximum using the first and second lerivative tests for f (x) = xª – x² +…

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Q: = = √²* (t²³ + 5t² + 4) dt 0 If f(x)= then f''(x) =

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Q: Compute and interpret f'(1) for each function above. f(r) = 6x2 + 3x 4 f'(1) = %3D

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Q: How does the interval of convergence (the derivative and the integral) behave.

A: The interval of convergence of the derivative and the integral is discussed here.

Q: Let f(x)=2x^2−4x+14.Findwhere f(x)>0.

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Q: Suppose f is differentiable and (-1,4) is a point on the graph of f. The estimate f(-0.8) 5 is…

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Q: Write a function that takes array inputs x, y and integrates using Simpson’s Rule. Do it without…

A: a=input("Enter value of a:");  b=input("Enter value of b:");  n=input("Enter value of n:");…

Q: Use forward, backward, and centered difference approximations to estimate the first derivative of…

A: We are given the function f(x)=5x5+3x3+2x+1 and the step size as h=0.5. As we are given no…

Q: Let f(x) = 3x2 - 2x + 4, find f''(x) and f''( – 4). = (x),.f Preview f''(– 4) =

A: Answer is both value is 6 and explanation is given below in the image.

Q: If I have a continuous, smooth (no sharp points) function with 3 local maxima and 2 local minima,…

A: Since the function is continuous , with 3 local maxima and 2 local minima.the function will have 5…

Q: f(t) = 2t³ + 3t2 - 36t

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Q: Find the critical pts, max., min., intervals of increase, intervals decrease, absolute max.,…

A: The give function is: fx=2x3-9x2+36 Find the critical point.

Q: Find f'(1) if Aæ) = (x² –-x²-x+1)(x² + 1). 1 O 2 O -3

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Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

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Q: The moment generating function of X is given as follows: M(x)(t)= e^(8t). Use the moment generating…

A: It is required to calculate the mean of the random variable X, using the moment generating function.

Q: please differentiate the function

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Q: Given that f(x) = x¹²h(x) h(-1) = 2 h'(-1) = 5 Calculate f'(-1). | Hint: Use the product rule and…

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Q: Determine the derivative of f(x) = 2.72²+3 Select the correct answer below: O (8x)72x²+3 O (8x In…

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Q: 16. r(0) = sec 0 tan 0 – 2eº -

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Q: The Population of a small town,p, is modelled by the function p(t)=10 050 + 255t-20t^2, where t is…

A: Solution :- p(t)=10050 + 255t-20t2 (a) The average rate of change of a function ft on an interval a,…

Q: if the implicit function is x3=at2, find the d2x/dt2

A: if the implicit function is x3=at2, find the d2x/dt2