Find a power series for the function, centered at c. 1 h(x) 1 C = 0 8x' h(x) = n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)

Q: Evaluate the definite integral that represents the volume of the solid formed by revolving the…

A: Explanation of the answer is as follows

Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = t = 0 T(0) = N(0) =

A: Unit tangent and normal vector

Q: Problem 6. The area A of a triangle is given by A=ac sin B, where B is the angle between sides a and…

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Q: Find the area of the region bounded by the equations y= x and Y3D6X-x². Note: theses are conics.

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Q: Evaluate the integral. n/2 5 cos?0 de

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Q: Find the arc length of the parametric curve. x = 7 cos(t), y = 7 sin(t), z = 24t; 0<t< T L =

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Q: 1. F'(x) = 2x ; F(1) = 2 2. F'(x) = 4x +1; F(2) = 6 3. F'(x) = 3x² + 2 ; F(-3) = -32 4. F'(x) = 4x³…

A: Apply integration both side with respect to x

Q: Find div F and curl F if F(x, y, z) = xz*i+ 6y°x*j+4z²yk. %3D div F= curl F=

A: To find the divergence and curl.

Q: d d Calculate r:(t) · r2(t)] and r:(t) × r2(t)] first by differentiating dt dt the product directly…

A: r1(t)=cos(t)i+sin(t)j+3t kr2(t)=2 i+t k

Q: dx a sin x+b cos x

A: Given problem:-

Q: xe*y dy dx

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Q: Evaluate the double integral over the rectangular region 4(a sin(y) – y sin(æ)) dA; R= {(x,y) : 0 <…

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Q: If g(x) J.J S. 1 -dt , find g'(2).

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Q: Question * Determine the nature of convergence of the following improper integrals 00 1 dx 1+ x* A =…

A: ∫a∞f(x)dx=limR→∞∫aRf(x)dx  If the limit exists and is a finite number, we say the improper integral…

Q: 11 Evaluate the iterated integral. JJ, J, (x² + y² + z?) dx dy dz A 5 в) з D 10 00

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Q: 17. Let y = 4t + 3, t = 6e and s = 1 + In x. Find dy in terms of x. dx %3D

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Q: Express the iterated integral as an equivalent integral with the order of integration reversed.…

A: Express the iterated integral as an equivalent integral with the order of integration reversed.

Q: Question 16 Use a triple integral to find the volume of the solid. The solid bounded by the surface…

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Q: Consider the following algebraic functions. F(x) = -x2 + 6x + 5 g(x) = x+ 5 Sketch and shade the…

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Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X y² +…

A: We have to find the volume of the solid.

Q: 4. Under the usual addition 47Z/2021Z .

A: A detailed solution is given below.

Q: 5. Find a Taylor series expansion around x = 1 for f(x) = 6. Without solving the exact answer,…

A: 5) The Taylor series formula around x=1 is:…

Q: Evaluate the integral. NOTE: Enter the exact answer. xe* dy dr =

A: the integration of the double integral is xexy.

Q: test the converg ence and divergence 27-1 2. (2h-1):

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Q: Describe the graph of the equation: r = 5ti – 8j + (1 + 5t)k. [Choose the correct answer.] O The…

A: Given, r= 5ti -8j +(1+5t)k Therefore, The equation is given by, r= &lt;0,-8,1&gt;+t&lt;5,0,5&gt;

Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = TT, using 4…

A: Here, the interval [0,π] is divided into 4 intervals of the length of each interval is ∆x=π-04=π4.…

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -180 J-120

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Q: Find the surface area of that portion of the surface Z = 4 -x that lies above the rectangle R in the…

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Q: d d Calculate ri(t) · r2(t)] and [ri(t) x r2(t)] first by differentiating dt dt the product directly…

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Q: Find the directed distance from the given line to the given point. (-1, 6) (5, 4) (10, 8) (1, 2)…

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Q: Which of the following angle measure (in degrees) is coterminal to an angle of measure 660 degrees?…

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Q: Question 9 1 2 1 Evaluate the iterated integral. J, J. J. (x²+ y2 + z?) dx dy dz -1°0 0, А) 5 В) з 8…

A: The solution is given in the next step.

Q: Find the exact arc length of the curve 1 (y² + 2)² from y 1 to y = 5. X = Enter the exact answer. L…

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Q: Evaluate the integral. NOTE: Enter the exact answer. c10 1 xe"y dy dx

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Q: Question 11 /4-x² c 3-x²-y² STS xdz dy dx Evaluate the iterated integral. J. J. -5+x²+y? 0, A)…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 6…

A: A detailed solution is given below.

Q: Find the centroid of the region. NOTE: Enter the exact answers. (ë, g) = | (?,?) y = z

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Q: V4-x² 3-x²-y² Evaluate the iterated integral. J. x dz dy dx -5+x?+y?

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Q: y=x*(1-x)ª 4-4x 4+4x

A: Use the chain rule of differentiation.

Q: Find the area of the region enclosed by the curves y = x² and y 4.x by integrating with respect to…

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Q: Use the Laws of Logarithms to rewrite the expression below in a form with no logarithm of a product,…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction to PQ

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Q: a 0 0 0 0b0 0 0 0 c 0 0 0 0 d Using cofactor method, prove that det M = = abcd

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

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Q: first octant 2 4- x+y dy dx -

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: Let's find.

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

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Q: Show that ā b 12

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Q: Find the area of the region inside the circle r = 24 sin 0 and outside the cardioid r = 8 + 8 sin 0.…

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Q: Use the arc length formula to find the length of the curve y = 3x – 5, -2sxs 3. Check your answer by…

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