As per the trigonometric substitution x = 4 sin 0, the following triangle is obtained. sin 0 = X x² 16x² (16-x The indefinite integral is X cos = V 16- X 4 Rewrite the equation in terms of x. 1- 8 1/2 J dx = 8 arcsin x² 16x2 dx = X XV 16- X 4 + C

Q: Work Problem 2 [ 31 (a)[3 Find a vector equation and parametric equations for the line that passes…

A:

Q: Use differentials to approximate the value of the expression. Compare your answer with that of a…

A:

Q: Work Problem 1. J (a)i- Show that the following equation represents a sphere, and find its center…

A:

Q: The arithmetic sequence bn is defined below. Find b3. b1=-2 D=-4 B3=?

A: The objective of the question is determine the b3 of given arithmetic sequence.

Q: Find the average value of f(x) = Enter the exact answer. fave = x (6x² + 5)² over the interval [0,…

A: Avg value is given by below

Q: Q.2: Find the trigonometric Fourier series of the periodic function f(t), and show if it is odd or…

A:

Q: The data given in the Table below is produced from a Linear Difference Equation model of the form: Y…

A:

Q: Consider the function f(x)=√/2x-8 for the domain [4, co). Find f(x), where f¹ is the inverse of f.…

A:

Q: Part 1 Basic Integration Solve the following integrals through video presentation. 1. f(4x²-3x²+) dx…

A: I can solve it but i can't explain like video presentation. It's a basic integration. Just apply…

Q: Find the area of the surface generated when the given curve is revolved about the given axis. 1 3 y…

A: y=8x13, for 0≤x≤18, about y-axis

Q: Let f(x) = { 2x-3. 3x²+2, if x < 3 if x ≥ 3 be a piecewise function. Evaluate Sof 0 f(x)dx=

A: We can find the integration of the piecewise function as below.

Q: b = 2i + j + 3k 14 direction of a = Select one: O True O False is the unit vector in the 2i + j + 3k

A:

Q: The equation of the plane that passes by P(-1, 2, 1) and that is perpendicular to the line x - 3 1-…

A:

Q: A - 3 In 1x³ 3x²1+C BIn 1x³ 3x²1+ C x²–2x x3 3x² C dx In 1x³ 3x²1+C In 1x³ 3x²1+ C -

A: The given integral,    ∫x2-2xx3-3x2dx

Q: Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x+6/(x^2+6)^1/2 Find…

A: See this solution in below

Q: The symmetric equation of the line that passes by P(1, -1, 1) and Q(3, 2, -1) is: Select one: x-1 0…

A: This question can be solved using the concept of lines in three dimensional geometry.

Q: Set-up and evaluate the triple integral for the mass of the box 1≤x≤2, 1≤ y ≤16, 0≤z≤ with density…

A:

Q: 2. Approximate √64.1 by using linearization and use a calculator to compute the percentage error.

A:

Q: The definite integral is equal to Select one: none of the others 02 -16 [²(3x² + 4x³)dx O-8 0-6…

A:

Q: Q.1: Solve the differential equation below; xy' + 4y = 8 x¹

A: We have to solve above differential equations

Q: Switch the order of integration of the following integrals, then evaluate: ƒ ƒ x sin(y²) dydx = x=0…

A: Explained below

Q: The vectors u = (5, -4,0) and v = (-4,-5, 4) are orthogonal. Select one: O True O False

A:

Q: An open-top box is to be made from a 18-inch by 42-inch piece of plastic by removing a square from…

A: Diagram of the mentioned box will  be as following

Q: b) [. Provide two points on the sphere that you have in part a. c) [. The intersection of the sphere…

A:

Q: Evaluate: 10 sin(3x)dx None of them -0.532 -0.253 0.253 -0.235 0.0235 -0.325

A: The given integral is:∫π6π4sin3xdxWe need to solve the above integral.

Q: Q2 a) Find the parametric equation of the line that passes by P(1, 2, 2) and that is parallel to the…

A: We have to solve above question of vector and 3D.

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 6 x+8 dx Write your answer exact…

A:

Q: A. ſºf(x)dx = B. If the vertical red shaded area in the graph has area A, estimate: ſ'ƒ(x)dx = (Your…

A: The graph is given as ,

Q: Find r'(t). r(t) = (3 cos(t), 4 sin(t)) r'(t) = (No Response) Need Help? Read It Watch It

A:

Q: 클 ~D f(x) = x² e² е (12) Find f '(x). f'(x) = x²²²e² + e² 2x² f" (x) = X

A:

Q: Find r(t) for the given conditions. r'(t) = 8e4ti + 5etj, r(t) = (No Response) Need Help? Read It…

A:

Q: f(x) = (x + 6)2/3 (a) Find the critical numbers of f. (Enter your answers as a comma-separated…

A: Given that fx=x+623a.find f'x=0 and solve x is a critical numbers.fx=x+623f'x=23x+6-13f'x=23x+613so,…

Q: Let f(x)=(3x(^2) -4x+5)(^100) -((2x+1)/(x-3))^5. Calculate df/dx

A: We can find the derivative as below.

Q: Find the Maclaurin series of xe³x. Σ n=0

A: Find the maclaurin series of x9e3x.

Q: Calculate the derivative of y with respect to x. Express derivative in terms of sin (y³) (Express…

A:

Q: Let R be the region bounded by y = x², x = 1, and y = 0. Use the shell method to find the volume of…

A:

Q: Evaluate the indefinite integral: + 1+x8 dx

A:

Q: onds and S(1) is the distance in feet from the top of the building. What was the average speed of…

A: topic :- application of algebra

Q: A graphing calculator is recommended. Consider the function below. (If an answer does not exist,…

A:

Q: Evalute ff Rx²dA, where R is the region in the first quadrant bounded by the hyperbola xy = 16 and…

A: The given integral: ∫∫Rx2dAWhere R is the region in the first quadrant bounded by the hyperbola…

Q: If f '(x) = 0 and f"(x) <0, then the point (x, f(x)) is a local minimum. a) always b) sometimes c)…

A: Please note that following the guidelines only one question is to solved.

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

A: Topic = Series

Q: Use logarithmic function to find dy/dx, if y=(x^2+5)^sin (2x)

A:

Q: The definite integral is equal to Select one: lò xác thỉ xác Of xdx + ² xdx Of xdx + xdx Of xdx -f²…

A:

Q: The force exerted by an electric charge at the origin on a charged particle at the point (x, y, z)…

A:

Q: Consider the following graph on the interval - 165° < x < 270°: 5 4 3 2 D 1 150-120 90 -60 -30 -1 -2…

A: We have given a graph of function and finding amplitude,period and function

Q: f₁(x) = 8, f₂(x) = cos²(x), f(x) = sin²(x) g(x) = c₁f₁(x) + C₂f₂(x) + C3f3(x) Solve for C₁, C₂, and…

A:

Q: he line integral of the vector field F= over the curve C which is the quarter of the rcle from…

A:

Q: Verify that the function satisfies the three hypotheses of Roll's Theorem on the given interval.…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the arc length of the curve below on the given interval. 3 1/3 3.5/3 y = 5x +9 on [1,27] The…

A: The given curve,    y=35x53-34x13+9 on 1,27