Find the volume of the solid that results when the region enclosed by the given curves is revolved about the x-axis. y = /100 – x2, y = 8 NOTE: Enter the exact amswer. V =

Q: Let A = (1, 0, 2) and B = (6, -2, 3). Find projaB.

A:

Q: Find the area of the surface. the part of the surface z = xy that lies within the cylinder x? + y² =…

A:

Q: Using Integration By Parts, x sec - x tan x dx = %3D

A: Use integration by parts.

Q: x+V x+V X lim X- 00 V> V x+1 х+1

A: To evaluate: limx→∞x+x+xx+1

Q: Using integration by parts, which of the following options is true x arcsec x dx ? xdx A. * Arcsec x…

A:

Q: 5. Let f be a function satisfying the following properties: continuous on R \ {0} • f(-1) = -3 •…

A:

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A: The given function,   f(x)=1x+ln x, 0.6≤x≤5

Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 31.…

A:

Q: Find exactly T(t) and N(t) for x = e*cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A:

Q: Describe the graph of the equation. r = 7 cos ti – 18 sin t j+ k O An ellipse in the planex = 1,…

A:

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A: We find the local extrma using first derivative test by checking the nature of f'(x) at different…

Q: Q5/Find the Laplace Transform -3 4- f(t) = V2t E) = va Where r %3D

A: To find the Laplace transform of given function.

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 11 cos(t)i + 10 sin(t)j +…

A:

Q: Find the function f(x) such that f''(x) = 6x + 3 cos(x), f(0) = 5, and f(1) = 2 − 3 cos(1).

A:

Q: 41. Suppose that both f and g have inverses and that h(x) = (f o g)(x) = f(g(x)). Show that h has an…

A: Explanation of the answer is as follows

Q: Determine the general equation of the plane 2 passing through the point P (1, -4, -5) and parallel…

A:

Q: dx Using Trigonometric Substitution find f(0) 3 (x² + x + 1) 2 4 3 sec? e O 3 sec? e 4 O 3 sec e 4 3…

A:

Q: By about how much will g(x,y,z) = x + x cos z -y sin z + y change if the point P(x,y,z) moves from…

A:

Q: Evaluate sin*(2x)dx. sin (2x)dx. sin 4x, sin 8x + C 64 3x 8 8. sin 8x + C 64 O X sin 4x 4 8 8 O 3x +…

A:

Q: What are the polar coordinates of the point P shown below? 2 3 4

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

Q: Using Integration By Parts, x3 x2 +4 dx = uv- - Sv du

A:

Q: A continuous function y f(x) is known to be negative at x = 2 and positive at x=7. Why does the…

A: Given that f(x) is a continuous function.

Q: In how many ways can the digits in the number 8,400,000 be arranged? ways (Type a whole number.)

A:

Q: 32 (c) Show that Hence, find the interval for x that satisfies the inequality = 22* 2 x 4" 32" -…

A:

Q: |(x+3)°(x+b)d dx is In 3x2 +8x– 12 The resulting integral of + C, where a, b, d, and e are integers.…

A:

Q: 2х n evaluating J cos²(2x) Tx using integration by parts, identify the portion of the integrand to…

A:

Q: Assuming that z is a function of x and y, find the equation of the tangent plane and the equations…

A:

Q: _14. Suppose that a function f: R² → R and its partial derivatives up to the third orders are…

A:

Q: Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that…

A: Given problem:- Use the method of Lagrange multipliers to find the dimensions of the rectangle of…

Q: 3x2 + 7x + 28 A f(x) Using partial fraction, evaluate x3 + x2 + 7x dX, the decomposed fraction is x2…

A:

Q: QUESTION 17 2x³. Consider E* s2x²-x²+x+2 x4 + x³ D dx find A+B+ C+D- dx = x2 X +1 0 5 2. O O O O

A:

Q: Ca

A: ∫92-x22dx=∫81-x22dx=∫ 6561-162x2+x4dx=∫ 6561dx-∫ 162x2dx+∫ x4dx=6561x-54x3+x55Add a constant to…

Q: x² + 2x- 10 (2 dx = x² (x² + 4x + 5) (2x + 4) + 1) (2x+ 4) +1) x2 + 4x + 5 x2 2 Consider dx -…

A:

Q: Given : S 6x³e**+3 dx. Using integration by parts (S udv = uv - fvdu) and letting u = f(x), dv =…

A:

Q: 5xy = 4x²z – 3yz²; xz and xy.

A:

Q: x² – 1 lim x→1 /x – 1

A:

Q: 1. Evaluate the following limits. 2 - V2r + 10 a. lim 1-3 x2 + x – 6 4x – 7 lim z+-1- \3x2 – 2r – 5…

A:

Q: s-8 3. (s-3)(s²+2s+17)

A:

Q: За — 1 (x – 2)(x + 5)

A:

Q: 3(x + 2)\/1 (x+2)² Which of the following is *+2) + arcsin 9 +C equal to? arcsin (z + 2) + (x + 2)v5…

A: Given that,     92arcsinx+22+3x+21-x+2292+C

Q: sec(0) Compute the area A bounded by the line r = 7 e and the rays 0 = 0, and 0 = 4 as an integral…

A: Here, the formula used is: A=12∫abr2dθ

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 2 1 lim t++00 \ 5t2 + 6'4t (?, ?)

A:

Q: dx The result of is F(b) – F(a), where F(a) and F(b) are both real numbers. What is the value of F…

A: integration

Q: Question 4 of 10 Find the volume of the solid that results when the shaded region is revolved about…

A:

Q: Complete the following KenKen puzzle to determine what is represented by x and y?

A: The rules of KenKen puzzle is: Use each number only once per row, once per column. Cages with just…

Q: Given that lim f(x) = 0 Xa lim g(x) = 0 Xa lim h(x) = 1 lim p(x) = ∞ Xa lim g(x) = 0, evaluate if…

A:

Q: Find the volume of the solid that results when the region enclosed by 2.x y = e2, y = 0, x = 0, x =…

A:

Q: If you are going to evaluate the integral f dx using trigonometric substitution, the answer is 2(tan…

A:

Q: (2x+4) + 1 x² +2x- 10 dx = x² (x² + 4x +5) (2x +4) +1) dx- x² + 4x+5, Consider dx evaluate | x² + 4x…

A:

Q: 5x -dx? J x³ + x² + 4x+4 How many quadratic and distinct factors are in the denominator of

A: