1 - dx is approximated using the trapezoid rule and Simpson's rule, the error is less than Use the error formulas to find the smallest n such that when 10-6. (The error formulas are given below.) When using the trapezoid rule, n must be at least The errors E in approximating f(x) dx are: (Ь —а)3 Trapezoid rule: E < - [max |f"(x)|] , a < x < b 12n? (Ь — а)5 Simpson's rule: |E < nax f(4) ,a < x < b 180n4

Q: Differentiate the function. g'(t) = g(t) = In t(t² + 1)8 3 4t 1 -

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Q: 8 If f.°³ F(x ³ f.° 9(x. f(x) dx = 39 and 8 d fº[31 g(x) dx = 16, find [3f(x) + 5g(x)] dx.

A: NOTE: Refresh your page if you can't see any equations. . here we have ∫08fxdx=39 ∫08gxdx=16

Q: If L(f(x) – 2g(x))dx = 12 and g(x) = x, find f(x)dx. Hint: draw a sketch of g(x)! %3D

A: We have ∫28(f(x)-2g(x))dx=12g(x)=xWe have to find∫28f(x) dx

Q: '5 Given f(x) dx = 16 and f(x) dx = 8, evaluate (a) f(x) dx. 0. (b) f(x) dx. 5 (c) f(x) dx. '5 (d)…

A: Solved below

Q: 8. For f(x, y) == xex²y Find fx (1, 2) {needs product rule}

A: Explanation and some important formulas:

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Q: 6. For f(x, y) = x²exy Find fx (2,1) {needs product rule}

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Q: dx (x-2)V4x²-16 is equal to 2 - -1 + C 4 sec

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Q: x +1 dx x(x² + 4)' (f) | #(2² + 4) ع و ش

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Q: Let f(x) = 5 + V4x - 6. Find f (x). f (x) =(-5)2 + 6 Add Work Calculator Check Answer

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Q: 2) (6 pts) Find the tangent line through the function g(x) = 6 -√√x when x = 4.

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Q: 9 | f(x) dx = 2. Find 8. f(x) du . 8. 3) Suppose that 6f(x) du and 8.

A: Answer

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A: Given,

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A: ∫(18x2 + 3)(6x3 + 3x)6dx We have to use u-substitution for the above function. To solve this, u is…

Q: 8. Suppose that f f(x)dx = 5, f² f(x) = −3, ſª g(x) = −1, and g(x) = 2. What is * (4f(x) — 3g(x) dx…

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