8. Find the volume of the solid generated by revolving the region bounded by the curve y = 4 – x² and the line y = 2 – x about the x -axis.

Q: Matching Type. Match Column A with Column B. Write the letter of your choice from Column B in the…

A:

Q: Solve the given third-order differential equation by variation of parameters. y"+ 64y' = sec(8x) |3|…

A:

Q: After a fall, a 79 kg rock climber finds himself dangling from the end of a rope that had been 13 m…

A: We have to find stress, strain and Young's modulus.

Q: xdx + ydy = (x² + y²)dx

A:

Q: Solve the following differential equations using the method of undetermined coefficients. y" – 2y" +…

A:

Q: X1 – 4x, + X3 = 2 4x1 + X2 =1 Xz + 4x3 =-1

A: Since the question is asked to solve by two different method solution by one of the method is given…

Q: 0,81 - 0.3104 + 27, wheret is the time in hours after When a factory operates from 6 AM to 6 PM, its…

A: Given problem:- When a factory operates from 6 AM to 6 PM, its total fuel consumption varies…

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Solution is given below

Q: Find two unit vectors in 2-space that make an angle of 45° with 9i + 4j. NOTE: Enter the exact…

A: Solution: Let u = ai+bj makes an angle of 45 degree with v = 9i +4j

Q: Perpendicular to the plane z + 3y – x = 7 and containing the points (2, 5, 0) and (0, 2, -1)

A: Solution of question is written in below steps.

Q: Discuss the continuity of the function on the closed interval. Function Interval 9 - X, f(x) = [-3,…

A:

Q: 4. The function g(t) = (8t)* – cosh² t + sinh? t satisfies g'(c) = 0 for which value of c? %3D (a) c…

A:

Q: dx 25. Integrate: S Ve-2x –1 А. Sec-1e* + С В. Sec-1е-* + С С. — Sec-1e* + С | D. —Sec-1e-* + с

A:

Q: in. The length of the square-end edge is in. The box height is The greatest volume of the box is…

A:

Q: 13 dt 9+6t 4 (9+6t)5

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: S sin x In(cos x) dx

A:

Q: Determine the interval(s) on which the function is continuous: 2r+ 7 212-3x-9 if x 1/2 Ox1/2 Ox1/2…

A:

Q: Solve the following differential equations using the method of undetermined coefficients. y" + 4y' +…

A:

Q: 17 + sin w sin(1+ cos w)) dw 7-2w

A:

Q: Find k if the shortest distance from (-2,5) to the circle x2+y2+kx+4y=12 is 3.6 units. a) 5 b) 6…

A: Find K.

Q: Find two unit vectors in 2-space that make an angle of 45° with 7i+ 6j. NOTE: Enter the exact…

A:

Q: Test your understanding. Write TRUE on the space provided if the statement is correct and FALSE if…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Give the curve r = 3 cos 0 b) Find the points on the given curve r = 3 cos 0 where the tangent line…

A:

Q: Determine whether the sets S, and S, span the same subspace of R. s = ((0, 0, 1). (0, 1, 1), (8, 1,…

A:

Q: Determine the critical point and find for the maximum and minimum values at closed interval for the…

A:

Q: Find an equation of the plane that passes through the points (-2, 1, 1), (0, 6, 11), and (1,0,-1).…

A: Given

Q: Determine whether the lines Lj and L, are parallel. Lj: х%3D 3 — 31, у %3D 5 + 1, L: х%3D6 — 9t, у…

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A:

Q: Differentiate the following using logarithmic differentiation. 1. у%3D (x+6)(x+8)8 (r+3)3(r+5)s

A:

Q: Evaluate the given: So sin" () cosº () dz cos 10

A:

Q: (6) At the start, an experiment records 1 gram of bacterial culture, and the culture's weight is…

A: In logistic growth, a population's per capita growth rate gets smaller and smaller as population…

Q: 1. Consider the function f(x) = x - 4 on the interval [-2,2]. Calculate the Riemann sum using: a.…

A:

Q: Choose the correct answer. 1. The sequence (x) = (-n) is. a) Cauchy b) bounded e) divergent d)…

A: We have1) The sequence (xn)=(-n) is . . . . . . . . .Now we have take n=1 x1=-1put n=2x2=(-2) So, we…

Q: Find the area bounded by the curves y=8x-x2 and y=x2, and the line 4x-y=-12.

A: I have appended the formula used in the solution part.

Q: Let A = (1,0, 2) and B = (6,–2, 3). Solve for projĄB.

A:

Q: find of the f llowing 2. 2 -5x*

A: Solution of question is written in below steps.

Q: -1 Cos'x 4. | X. dx 1-x* 2 dx 3 (x² + 2 + 2x + 2)2 5.

A: 4). Given: I=∫cos-1x1-x2dx    ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: Part 3. Provide solution in finding the derivatives of the given function 1. y= 4x5-2x + 3x- 10 2. y…

A: Let's find.

Q: y 20 y=g(x) 10 20 35 Evaluate each integral by interpreting it in terms of areas. 10 (a) g(x) dx 30…

A:

Q: Given .5 8 | f(=)dz = /f(2)dz + f(2)da – | f(a)da, -6 6 what are the limits of integration a and b?…

A:

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(8,…

A:

Q: The figure shows the stress-strain curve for a material. The scale of the stress axis is set by s =…

A:

Q: Verify that the two planes are parallel. -x + 6y + 22 = B -글x+ 3y + z =9 Find the normal vector, n,…

A: I have appended the formula used in the solution part.

Q: u = 5i + 4j, v= 3i + 2j (a) Find the projection of u onto v. (b) Find the vector component of u…

A:

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z2 (2,…

A: We have to find maximum value of the directional derivative at the given point.

Q: What is the radius of convergence the power series solution to: for Cx?+Qx+17)y"+y?-y=0,centered at…

A: The given differential equation: x2+2x+17y''+y'-y=0 can be re-written as…

Q: .f (x) = cos(-x) .f(x) = sin(8x) .f (x) = 2 sin(-5x) a) f'(x) = 2 sec(2x – 1) tan(2x – 1) %3D - b)…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: true or false: if f’(x) = 0, then the point (x,f(x)) is an extreme point.

A: Given query is to find statement is true or flase.