Find the volume of the solid that results when the region enclosed by the given curves is revolved about the y-axis. 177 x = csc y, y 197 x = 0 4 A 8 pi B 6 pi 4 pi 2 pi

Q: 4. Let em² cos , 2.x + b, r 0 r>0 h(x) = %3D where b is a constant. (a) Explain why h(x) is…

A: We need to solve continuity problem.

Q: Find div F and curl F if F(x, y, z) = 8y°z³i – 11x*z°j – 3xy°k.

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Q: Which among the choices is NOT true about the continuity of f(x)? x2 -4x-5 if x + 5 f(x) = 2x–10 3,…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t? +9 1 lim t+oo 3t2 + 4' 6t = (?, ?)

A: 1/infinity=0 is used

Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabo arc y = x² from (0,0) to (1, 1).…

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Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = ti + t°j

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Q: Solve for the derivative of the following composite functions. f(g(x)) = (x+ 4)* 2 f(9(x)) = (2x2 +…

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Q: 3x. If sales are increasing ompany's revenue from selling a units of an item is given as R = he rate…

A: Given query is to find rate of change of revenue.

Q: Use sigma notation to write the Taylor series about x = xo for the function. e¬4x, xo 1 Taylor…

A: f(x)=e-4xf-14=ef'(x)=-4e-4xf'-14=-4ef''(x)=16e-4xf''(-14)=16ef'''(x)=-64e-4xf'''(-14)=-64e

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -9, 6) Radius:…

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Q: 2. Let f(x) be a continuous function on R. The following is known about f(x): • The domain of f(x)…

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Q: Describe the graph of the equation. r = 7 sin 6t i – 7 cos 6t j O It is a circle of radius 6 in the…

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Q: f(x) = x- 3, g(x) = x2 Find (f+ g)(x). (f + g)(x) %3D Find the domain of (f+ g)(x). (Enter your…

A: Topic:- function

Q: | (csc 0)(1+ sin? 0 + sin 0 cot? 0) do а.

A:

Q: Find curl(7z i + 8x j+ 5y k). curl (7z i + &x j+ 5y k) = ( i )i + (i )j + ( )k

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Q: Exercises Distinct Real Roots of Auxiliary Equation Find the general solution 5. (D² – 1)y = 0

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Q: Find V · (V × F), if F(x, y, z) = e"i+ 3ze'j – 5e"k. V. (V × F) =

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Q: -x lim + 169 x→-9 x+9

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Q: Find curl (6z i + 7x j+ 9y k). curl(6z i + 7x j + 9y k) = ( i )i + ( i )j + ( )k

A: Explanation of the answer is as follows

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise p…

A: As we know that; The Green's theorem; ∫CPdx+Qdy=∫∫D∂Q∂x-∂P∂ydA   Given: I=∫C3xy dx+6xy dy And C:…

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* r(t) = 8 cos(8t)i+ 8 sin(8t)j + 5tk…

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: This is a problem related to vector calculus. Based on the general formula of green's theorem we…

Q: Using Long (Euclidean) division then decomposition into partial fractions x4 – 4x2 – x – 3 | dx х2 —…

A: We have to find value of given indefinite Integration.

Q: For the given vectors a and b, find the cross product a x b. =(3,0, -1), b = (3, 2, 0) a %3D a x b =

A:

Q: b. In x? dx

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: The objective of the question is evaluate the definite integral using the Green Theorem.

Q: Find div F and curl F if F(x,y, z) = x°i – 2j + yzk. div F= curl F=

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Q: Use the formula «(t) ||r'(t) × r"(t)|| to find «(t). r(t) = e12i + e-j K(t) = %3D

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Q: A swimming pool full of water is in the form of a rectangular parallelepiped 5 m deep, 25 m long and…

A:

Q: INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) F(x) f'(x) lim = lim Еquation…

A: This question is based on L hospitals rule.

Q: Find the area bounded by the indicated curves. y = (x - 1)2, y = 8x - 24, where 3 s x s 5 Optional…

A: Let us draw the graph.

Q: Find the radius of convergence, R, of the series. xn + 1 3n! n = 2 R = Find the interval, I, of…

A: A detailed solution is given below.

Q: aluate the integral / (8 x + 18y)dx + (24x – y)dy alor y = x² from (0, 0) to (1, 1). TE: Enter the…

A: Topic:- application of integration

Q: 524–121x4 lim x00 62xº+24x4+234x³+11x2+169 ||

A:

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dx + 5x2y2 dy

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Q: Evaluate the integral (12x + 12y)dx + (9x - y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

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Q: for x[z] given by z1 x[z]: 1-z2 then X[00] equal to Select one: a. 0.5 b. 0

A: B is the correct option.

Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to…

A: For the arc y = x2 and the range of x from 0 to 1. So, dy = 2x dx. Now,…

Q: Find curl (5z i + 6x j + 8y k). curl (5z i+ 6x j + 8y k) )i + ( i )j + ( i i )k

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Q: Evaluate (2x - y) dx + (x + 5y) dy.

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Q: 2. Find the orthogonal trajectories of the family of parabolas y = cx O In(x² + y² ) = c O 2r? + y²…

A: Explanation of the answer is as follows

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(1) = i – 26j + %3D (a) r(t) 3ti- 2j + 2 k (b)…

A:

Q: 'ind V · (V × F) if F(x, y, z) = 9 sin ci + 5 cos(9x – 10y)j + 2zk. - V · (V × F) =

A: To find div (curl F).

Q: y" — Зу + 9у — 0

A: Given; y''-3y'+9y=0

Q: -Find Taylor or Maclaurin for the following functions: 1) f(x) = sin 3x

A: In this question we can find the Maclaurin series for the function. Maclaurin series for the…

Q: 1 Without a table of values and using index laws, sketch y 2*-

A: y=12x 2-1 y=12x2 y=22x

Q: tanx dx I+x?

A:

Q: Let 7(t) = Find a parametric equation of the line tangent to 7(t) at the point (7, 5, 1.386) x(t) =…

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Q: Describe the graph of the equation. r= (5 - 31) i - 10:j O tis a line in 2-space that goes through…

A: This is a problem related to vector. Based on the general formula and concepts we will answer the…