Make the indicated trigonometric substitution in the given algebraic expression and simplify (see Example 7). Assume that 0 < 0 < π/2. 1 x²√√16 + x² x = 4 tan(8)

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Q: q. r. √y² - 25 -dy, y > 5 y³ dx x²√√x²-1 2 ,x > 1

A: Solve both integral as following:-

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Q: A:-Find parametric equations for the lines, the line through (4, 7, 1) perpendicular to the vectors…

A: I am attaching image so that you understand each and every step.

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A: This question is based on solution of Homogeneous differential equation.

Q: If 2 [². then is equal to f(x)dx = 5 and Select one: O 15 O-5 O 10 none of the others -10 5 [³ 5 1₂…

A: We can find the correct option as below.

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A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y,z) = x² + y²…

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Q: Write an equation for the polynomial graphed below. You can leave the function in factored form. -5…

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Q: 2.) dy 1) = x - (²2²) y = x ² ex ; x = 1, y = 0 dx P(x) = = = = Q(x) = x² ex X Standard form: dy dx…

A: Given differential equation dydx-2x y=x2 ex  ; x=1 y=0

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A: We can solve the given problem by using the concept of derivatives.

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Q: 2. Use a double integral in polar coordinates to find the area of the region. (a) The region…

A: We need to find the area of the given regions using double integral in polar coordinates.

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Q: Problem 3. Solve below definite integrals b) [3te (b) 3tet²+1dt, In(x) 23 ©f! -dz, (d) TH In(x) dr.…

A: ∫ eu du = eu +C Note : As per our Guidelines , we can solve first question as your parts is not too…

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A: In this question we have to find the area of the surface generated by revolving the curve about the…

Q: For the function f(x) = 7x³ − 2x² + 2x + 9, find f''(x). Then find f''(0) and f’’(9). f''(x)= Select…

A: Derivatives

Q: True or False: We have Select one: O True O False 0 8 √√xdx = 12.

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Q: Question 3 Given the points A(-8, 2, 3) and B(-8, 2,-4). a). Write parametric and symmetric…

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Q: 2. Solve the following differential equations using variation of parameters: (i) y" + 4y = 4 tan 2x,…

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Q: Find the vector component of v=2i-j+3 kalong b = 6i+6j+7 k and the vector component of v orthogonal…

A: The vector compoent of v along b is:Projbv→=v→.b→b→ b→The vector component of v orthogonal to b…

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Q: on what intervak of x is the graoh is g(x) increasing? justify your reasoning

A: To determine the interval of x for which the graph of gx is increasing.

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A: We have to find the volume generated by rotating the region

Q: 1. Given the function F(x)= 3x-7, x < 4 (x² - 2x, x ≥ 4 I. lim F(x) exists. X-4 (mumixat endorf a)…

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Q: Prove the statement using the ε, δ definition of a limit. limx→3 (4x − 5) = 7

A: To solve the given problem. limx→3 (4x − 5) = 7

Q: 1. Evaluate the iterated integrals. In 3 In 2 (a) f f e** dydx S S 00 (b) ff X 00 (xy+1) dydx (c)…

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

Q: Solve 23x. 77 5x 4.2

A: Here the given problem is,              23x=4×25x We need to find the value of x.