Evaluate: sec²(4t) [3-tan(4t)]³ dt a.-16 [3-tan(4t)] + C b. | [3 –tan(4t)] + C 4 OC. 1 [3-tan(4t)] +C 16 O d.-4 [3-tan(4t)]ª + C O b.

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A: F(4) is the answer.

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A: To find the integral: ∫0∞x2e-xdx converges or diverges.

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Q: The Scot* dx is {A}-cot+3 csc-x+ C {B} cot ³+3 cot + x + C {C} cot+ 3 csc-x+ C {D} -cot ³+3 cot+x+C

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Q: - у = 3x-2 4x-5

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Q: 1 A tank with a capacity of 400 gal initially contains 100 gal of water with 50 lb of salt dissolved…

A: 100gal=Initial amount of water in 400gal tank50lb=Initial amount of salt in the tank1lbgal=salt…

Q: Problem 1: Obtain ODE by eliminating arbitrary constant A, B, and C y = A e2x + Be + C

A: To find out the ODE by eliminating constant A, B and C.

Q: (a) (c) 1² diz +1 cos(50) de (b) (d) √ X x² + 1 I √x+1 1 dx dx

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Q: Find the indefinite integral. Solution in handwritten. 1. f(-8x)√3-4x²dx

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Q: 10. Consider the region bounded by the graphs of y = tan-¹x, y = 0, and x = 1. Find the area of the…

A: Let's find.

Q: Let ₁1 and In+1 = limit. 1 for n N. Show that this sequence is convergent and find its In + 2

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Q: In the triangle below, BA=u and BF=v. Express each of the following in terms of u and v. a) CD b)…

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Q: 4 2 + Find the area of the portion of the Sphere x² + y² +2²= 9 between the planes Z=1 and 2 = 0.…

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Q: Use the formula k(t) = = k(t) = ||r' (t) x r"(t)|| (t)||³ ||r' r(t) = t²i+t⁹j = to find k(t).

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Q: PH Given: = ln(x²y-1); Find dy/dx.

A: Given xy=ln(x2y-1)

Q: Evaluate the iterated integral. [(x + y) dy dx

A: Here is the solution:

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Q: Question 10 Given: y = xcos (x); Find y'". O(E) None of these Oy" xsin (x) + 2 cos(x) Oy" asin (x) -…

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Q: ANSWER

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Q: \1/2 2. y = (2 tan² 20-1)

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Q: Emma thinks that three lines cannot be simultaneously perpendicular to each other. What can Emma's…

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Q: Determine the behavior of the functions defined below. Note that it is common to write "g(z) → oo"…

A: The given function is;  g(x)=-10x3+5x2+5. Repost the next parts.

Q: Find the indefinite integral. a. fsecy (tany - sec y )dy b. f(x²-9)(2x)dx

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Q: 8. eeer +eyty dy

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Q: 29. aj = x, a₂ = x+3 30

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Q: Sketch the region R and evaluate the iterated integral x, y) da. [²³²(¹-2x - 2x + 8y) dy dx

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Q: 3. Solve the linear system below using Cramer's Rule. a+b+c+d=13 2a + 3b c = -1 -3a + 4b + 2c + d =…

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Q: If F(x) = f(t) dt, where f is the function whose graph is given, which of the following values is…

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Q: Find the indefinite integral. Solution in handwritten. 6x² 1. Sa -dx (4x3-9)3

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Q: Ⓒ Given SS² +8 dy dx. Reverse the order of in tegration and evaluate. Draw the region.

A: In the given problem first we draw the region then reverse the order of integration and after that…

Q: A. Using chain rule find the derivative of the following functions. 1) f(x) = (x³ + 3x²) 200 2) f(x)…

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Q: Find the area of the region bound above by y = 2cosx and below by y = secx,-π/4 ≤ x ≤ 1/4.

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Q: ·SS v₂ Vx (2yi) •n do where S is the hemisphere x² + y² + z² = 9, z≥ 0. Use the normal vectors…

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Q: Direction: Provide a complete solution when necessary. A. Solve the following Systems of Non-Linear…

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Q: Evaluate the following integrals. 2. √x+ +5x² x4+5x³+20x+16 x(x²+4)² dx

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Q: Determine a for each arithmetic sequence. See Example 5. 33. as = 27, as 87 www 34. α12 = 60, 920 =…

A: A detailed solution is given below

Q: Find the line integral of f(x,y) = y ex² along the curve r(t) = 4t i + 3t j, −1≤t≤2. The integral of…

A: Use derivative for finding the line integral.

Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. 2 YA a. f*…

A: solution is given below..

Q: 2. Given So S√x y² +8 dydx. Reverse the order of integration and evaluate. Draw the

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