Complete the squares and locate all absolute maxima and minima, if any, by inspection. Then check your answers using calculus. f(x, y) = 32 – 8x +x? + 8y + y? f has aln) v at (i

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A: Given problem:- Find k(t) of r(t) =e12t i +e-t j

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Q: Distinct Real Roots of Auxiliary Equation the general solution (D² – 9)y = 0 (D² – 1)y = 0 -

A: Topic:- solution of differential equation

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Q: Perform the indicated multiplication on the differential operator D. Show your full solution.

A: We have to find out

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A: We have to evaluate given integral

Q: r=5 sin  18t  i−5 cos  18t  jr=5⁢ sin⁢  18⁢t⁢  i-5⁢ cos⁢ ⁢ 18⁢t⁢  ⁢j It is a circle of radius 1818…

A: We have to find the centre and radius of the circle.

Q: The equation y? = cx is a general equation of A. y' = 2 B. y = 2x 2x C. y' = y y D. y': 2y O A NONE…

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Q: 3 dy Зу =-sin -1 +C 4- 9y2 3 A True False B.

A: The given integral is 3/sqrt(4-9y2).

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Q: Solve for the derivative of the following composite functions. f(g(x)) = (x + 4)5 1.

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Q: Find the area of the plane region bounded byy x, x = -2 and x = 2. Answer:

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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: y" + y = sec 0 tan 0

A: The given differential equation is  y''+y=sec(theta)tan(theta).

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Q: if x 1. z +1 Given f(x) = 2x 1 Then, lim f(x)%= 2+1+ O does not exist O 2 0 1

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Q: Wage Gap Between Men and Women The bar graph shows the wage gap between men and women for selected…

A: To find G(10) and interpret it.

Q: Find curl (3z i + 4x j+ 2y k). curl (3z i + 4x j+ 2y k) = ( Di + ( j +( )k

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Q: 7. Sketch the region of integration, and evaluate the integral. 2 2x. JI zdz de dr .2

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Q: 7. Sketch the region of integration, and evaluate the integral. 22л г JI * zdz d0 dr 0 л 0

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Q: 3. Evaluate the integral 7/4 1 + cos²0 do cos²0

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Q: One of the correct. steps to evaluate x²inx. x²Inx dx to yield the correct integral (A dx x2Inx B x³…

A: The given integral,     ∫x2lnx dx

Q: Find the partial derivatives of f(x, y) = 5x*y². %3D

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Q: Find the general solution of y' =y sec x. A. y = C (secx+ tan x) B. y= C (sec x – tan x) C. y = C…

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Q: 25x?y" + 25xy' + y = 0

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Q: F (x) = f (t³ – t)°dt. Find the derivative of O 5(t – t)* (3t² –- 1) (23 – z)* O 5(2³ – z)“ O 3t2 –…

A: To FInd:  derivative of the given function

Q: 4. Evaluate •5 (4 – 2.x) dx - 2,

A: topic - definite integral

Q: The particular solution that satisfies the differential equation and the initial condition dy/dx =…

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Q: |y csc?y dy is equal to A) y coty+ coty B -у соty + coty dy C) None (D -y coty - | coty dy E у coty-…

A: we have to find out

Q: We need to enclose a rectangular field with a fence. We have 500 ft. of fencing material and a…

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Q: Find the general solution 1. (D² – D – 2)y = 0 2. (D² + 3D)y = 0 3. (D2 – 5D) + 4y = 0 4. (D² – 9)y…

A: 1. D2-D-2y=02. D2+3Dy=03. D2-5D+4y=0 Note:    Multiple sub parts are given, we are answer only three…

Q: Of the Sollds gene by Volving the regions Doundeu by graphs of equation given iines. y = 3x2 y = 0 X…

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Q: Which of the following is an antiderivative of f (x) = 52x? O (In 5) 52z – 1 52z +3 In 5 52 - 2 In 5…

A: we have to find anti derivative.

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A: We have to find out integration

Q: In t+1-2 dt, if we let V Vt+1-2, then dt is equal to 4x(x²+ 2)dx B (4x³+2)dx None D 2(x²+2)dx E…

A: To find out the dt.

Q: fu)=Sin(x) aニT R=?

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

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Q: dt, if we let V Vt+1-2, then dt is equal to A (4x³+2)dx B None © 2(x²+2)dx D 4x³dx E 4x(x²+2)dx

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Q: Find the volume of the solid generated by revolving the region about the given line. The region in…

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Q: **. . AY .. ... Use the shell method to write and evaluate the definite integral that represents the…

A: A detailed solution is given below

Q: The absolute value of the complex number [2 + sqrt (2) + pi] +j [e- sqrt (3) + 5] O 8.88 O 11.5 O…

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