b. ƒ(x) = x² ln x + sec x; find f"(x). c. f(x)= x³ sin x; find f(4)(x).

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A: 5y+10 = 4y-10 Now add 10 to both sides then we have, 5y+10+10 = 4y-10+10 5y+20 = 4y Now subtract 20…

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A: The given function is;  f(x,y,z)=xyz x2+y2+z2=243.

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Q: Solve the following equation exactly where 0 < 0 < 27. -10 cos 0 = –2 – 6 cos 0 %3D Select all…

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Q: 2 dt 22. Evaluate o v9– 2t² 2 dy 3-y³ 24. Evaluate o v8-y'

A: 22)I=∫0129-2t2dtt=32 udt=32 duI=∫29-9u2 32duI=2 ∫11-u2 duI=2 sin-1uI=2 sin-12 t301I=2 sin-1(23)

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Q: +2

A: To evaluate the given integral.

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A: Given f(x,y,z)=2x+y-2 ...(i)  subject to the constraint x2+y2+z2=.4....(ii) So the Lagrange function…

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A: Here, f(x)=3x2-2x+2

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A: Let's find.

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Q: 1. Find the Laplace transform of eat and 1 for t is greater than or equal to zero.

A: follow the procedure given below.

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Q: Consider a triangle ABC like the one below. Suppose that a=14, b=10, and A=82°. (The figure is not…

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A: Solution :∫cos7xdx∫cos6xcosxdx∫cos2x3cosxdx∫1-sin2x3cosxdx

Q: 2. Let A = (1,0, 2) and B = (6, -2, 3). Solve for proja B. %3D

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Q: (2) Find the full Fourier series for the periodic function ƒ : R → R defined by ƒ(x) = 1+ |æ| on the…

A: the fourier series expansion is as follow

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Q: 5. Use differentials to find the approximate value of [(5. 99)² + (8. 03)²+ (4. 98)]' decimal…

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A: Use the method of substitution and solve the integration.

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A: Solution-

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Q: . Integrating factors found by inspection.: y(x² – y² +1)dx–x(x² – y² -1\dy = 0

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Q: Consider the following IVP: y"+a2y = 0; y(0) = 1, y'(0) = 0   Find the general solution

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