dw a) Find for the following function. dt w = 2ye* -In(z), x = ln(t2 + 1), y = cos(2t + 2), z = et at t = 1 b) Find the mixed partial derivative at the point (1, 2). g(x, y) = sin(x) In(2y) + y ln(x) + 2xe³x c) Find the local maxima, local minima, or saddle points for the following function f(x, y) = x3³-y³ - 2xy + 6 d) Find the derivative of f(x, y, z) = 4zx³ - xy² - z in the direction of v=4i-5j +√40 k at P,(1,0,2) 81-3

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A: Given integral I=∫0π4  x3(x2+4)52 dx

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Q: 2z+8 (z+7)4 dz

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A: Given; h(t)=-4.9t2+91t+164

Q: π/4 ²dx (x²+4)5/2 (Use trigonometric substitution)

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A: Solution of the problem as follows

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Q: 1o. 1 |x-3|dx

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Q: Consider S 1x². 2-9 x3 what is the integral form in terms of ? A / Scos² e de Ⓡ = sin²e de B C…

A: This question is related to Indefinite integration, we will solve it using given information.

Q: Describe the long run behavior of f(t) = As too, f(t) → ? v As t→→∞o, f(t)→→ ? - 4tº + 2t6-3t5+1

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Q: e2x+Inx² sin x² dx -+fe²x cos x² dx

A: This is a problem related to integration. Based on the general formula we will solve the problem.

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Q: Test for convergence: Summation from n = 2 to infinity of (n + 3) / (2n^3 - 6)

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Q: Using trigonometric substitution, what is sec-1 (-) √x²-9 6x² + C sec (1) √x²-9 6x² + C sec-¹ √x²-9…

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Q: sin³ (cos(4) dx 2 32 Ⓒcos A COS 35 32 B 35 32 Ⓒ-3 cos (4) C 32 D 3/7/7 C (4)[-5cos (4)+7] 5³ (4)…

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Q: 2.4 x cos x² dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Given circle , With center at origin (0,0) And a point on circle is (4,3)

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Q: II. Determine if [x+1]. if x < -1 S x + 1 f(x) = 2 tanh (x+¹) if 1<x< 1 1-x In [cosh (x + 1) + sinh…

A: It is solved whether f(x) is continuous or not.

Q: Given the function f(x) = -6 x -9 Evaluate f(8) = Find a when f(x) = 3 I

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Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, ...…

A: Given ∫cos42t dt=At-Bsin2tcos2t+Dsin4tcos4t+C To Find 2A-3BD

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A: D4-1y=0

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Q: Using trigonometric substitution, what is f √x²_9 x3 A sec-¹(²) + √x²-9 2x² + C sec (-)- √x²-9 6x² +…

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Q: c. The region R enclosed by the curves y = x and y = x² is rotated about the line y = 2. Find the…

A: Using disc method, volume of solid is evaluated.

Q: f/² () sin cos (sin (²) dx (Consider initially the first 2 terms)

A: To evaluate: ∫0π2sinx3cos4x3sin2x3dx Let I = ∫0π2sinx3cos4x3sin2x3dx We know that  sinxcosy =…

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A: Absolute maximum and absolute minimum on closed interval [a ,b] : 1.) Find critical points of f(x) .…

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Q: Compute the quadratic form x Ax for A= Xx₁ 12 - a. x = b. x= 1 X2 a. x¹Ax= 3 2 [1] 10 C. X = and…

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Q: y=√√√5-√x

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Q: Using trigonometric substitution to solve: f sin 2x +C 8 cos x√3-cos²x 1 + C 8 secx√4-sin²x sin 2x…

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Q: 20 x³ dx (x²+4)5/2 (Use trigonometric substitution)

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Q: Evaluate 5 (²) 4. dy -2

A: ∫-2-1 (y-2)dy/y ∫-2-1 (y - 2/y)dy [ 2y3/2/3 - 4y]-2-1 -2i/3 - 4i +42i +42i -14i/3 +82i

Q: Using partial fraction in evaluating f(x) + What is f(x)? X x²+x+7* A 2x-6 7 ® 1/²(2x+1)= 1/²/2 B ©…

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Q: 25 125 Explain why you think the series - 2 + 5 - .... 2 8 converges to a 32 finite number or…

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Q: 60. (a) dx SI dt 1 + √t (b) de fint di dt

A: We can solve this as follows:

Q: ²1dx = f ( + g(x)) dx, then A + √² g(x) dx is equal to 12. -1 + In(5/2) 1 -1 -1 + In(7) A. B. C. D.

A: The given integral,  ∫x2-1x3+xdx

Q: 7. f(x) = 3√x; [1,4] 8. f(x) = x-2/3; [1,27]

A: We can solve this as follows:

Q: 12 || ti + t²j||dt = |

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Q: Compute the area bounded by the curve x=y²-2y and the line x-y-4-0₁

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Q: Given: (1+2x) ex dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the value…

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Q: Consider using the method of partial fractions to solve x²+x+1 rb Sa 2x²+2+x²+x - dx = [Af(x) – B…

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