Use Romberg Integration to evaluate | f(x)dx with 4-digit accuracy. Start with ho = 1. 0.25 0.50 0.75 1.00 f(x) 0.3989 0.3867 0.3521 0.3011 0.2420

Q: oulsy od bnil )=8), calculate the xp 8 Given that %3D value of [2x-g(x)] dx. (*)8 = (

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Q: Differentiate. y' = || y = eP(p + p√p) X

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Q: Estimate the error in evaluating the function f(x)= e2x* sin x near the point x = 1.396, if the…

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Q: Estimate

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Q: 35 If fis continuous and the nearest integer f(x) dx 126 , find f(7x) dx . Please round the answer…

A: We have

Q: If f(x) = = √2x+6, find f'(x). Find f'(2).

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Q: Differentiate f(x) = -O.1x - 0.15x³ - 0.5x² - 0.25x + 1.2 at x = 0.5

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Q: Let f f(x) dx = -3, f¹ f(x)dx = -4 and g(x)dx = 6 and ¹ g(x)dx = 2. Then evaluate * (7 f(x) — 28(x)…

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Q: Let f(x) = log2(3x). Find f'(1). %3D

A: To find f ‘(1).

Q: Consider the function f (x) = -x² + 10. Find the average rate of change in the interval -5 <x < -1.

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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: A natural cubic spline S for a function f i defined by: x3 x2 - 12 4 3. S(x) = x3 3x2 + ах 4 17 + ax…

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Q: Find F(s). F(s) =

A: Using Laplace Transform Table: Ltn f(t)=(-1)n dndsn Lf(t)

Q: f(x) = (In æ)³ f'(x) = f'(e) = %3D

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Q: 5. Calculate the average rate of change for f(x) at the given interval: f(x) = −x² − 3x + 7, 2 ≤ x ≤…

A: 5. Given that the function is                                      To find the average rate of…

Q: Given f(x) = 1x + 3 Evaluate f'( − 3) - =

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Q: (b) Use FTC to evaluate (x-x X-

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Q: For what values of x is fAx) = x' + 3x - 1 increasing? Explain.

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Q: -- Let the function f(x) have the property that f' (x) = x+1 If g(x) = f(x²) find g' (x). х-5 g'(x)…

A: Simply use the chain rule of derivative .