If. the.work.required to stretch a spring 3 ft beyond its natural length is 9 ft-lb, how much work is needed to stretch it 27 in. beyond its natural length? x ft-lb Enter a number. dback

Q: in Problems 43-54, calculate the definite integral, given that 61 x dx 3 x dx = 7.5 x² dx = 21 %3D

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Q: For each of the following functions, find the indicated derivative using the definition. f(x) : 1+ s...

A: Given query is to find the derivative of the expression.

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Q: What are the 8 extreme values (both max and min) of the fu

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Q: 3) = + sin (4) r = y(In y- In r+1)

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Q: Let   u=4i−j​, v=4i+j​, w=i+5j

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Q: Task: Find the general solutions of the following differential equations 1. 2x(y+1)dx + ydy = 0

A: 2xy+1dx+ydy=0

Q: Find the unit vector ey, where v = (9,0,7). (Give your answer using component form. Express numbers ...

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Q: H.W: Evaluate the integral 3. -4y)dydx x*ydxdy 1 -1

A: ∫xndx=xn+1n+1

Q: Directions: Study the guided solution to the given function. Fill in the blanks with the appropriate...

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Q: Let u = u(x, y), and let (r, 0) be polar coordinates. Then 1 || Vu||? = u; + u3 Use this to compute ...

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Q: Find the directional derivative of f(x, y, z) = xy + z° at the point P = (3, –2, –1) in the directio...

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Q: Exercise 15. Let f(z) cos z (z2-1)2 The residue off(z) at zo = 1 is a) – sin 1 b) sin1cos 1 c) -(sin...

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Q: Find the value of the derivative (if it exists) at the given extremum. (If an answer does not exist,...

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Q: Suppose that a company's sales volume y (in thousands of units) is related to its advertising expend...

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Q: Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium mus...

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Q: A tank is full of water. Find the work required to pump the water out of the spout. Use the fact tha...

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Q: If xy² – y3 = 5, find y'. y' =

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Q: For the following functions, find: 1. the critical values of the first derivative 2. the intervals w...

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Q: Obtain the general solution. (xy)dx + (x² + v²)dy= 0 OC- 2(x2 + xy + y?) OC- y^(2x² + y?) OC = y(2x2...

A: Given (x.y)dx + (x² + y²)dy = 0

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Q: Find the absolute extrema of the function f(x,y) = xy - x - 3y on the triangular region with vertice...

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Q: Suppose that a particle moves along a line with position function s(t) =2t^2 +3t+1 where s is in met...

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Q: Determine whether the Mean Value theorem can be applied to f on the closed interval (a, b). (Select ...

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Q: Consider the following. gtx)= 6x - 7; h(x) 1.7* Find the derivative of f(x) g(x) h(x). rm- (a²-7)(in...

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Q: 6) For a function f(x) = x³ - 3x2 -1 use the first and second derivative tests to: a) Determine the ...

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Q: Obtain the general solution. (x2 + y²)dx + (xv)dy = 0 O xy(x² + y?) = Cª O x*x² + 2y?) = c* + 2y-) =...

A: As the Given differential equation is Homogeneous differential equation .Put y=vx and solve the diff...

Q: (-5t -21 (i) Find the domain of f(t). (ii) Find the values of A and B if the function is continuous ...

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Q: that : f the pth, qth and rth terms of an A.P. are a, b and c respectively, prove alq – r) + b(r – p...

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Q: D. Differentiate the following. f(x) = 4x5 - 5x +x +8 g(x) = * --*+x' + v2 c. h(x) = V9x° + V7x7 + V...

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Q: dx (2x-3) V5-12x+4x²

A: use simple integaration concept.

Q: Solve the following initial-value problems starting from yo = 6 . dy 5y dt A. y = At what time does ...

A: This is a problem of differential equation. Based on the general method and initial value we will so...

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not ex...

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Q: Use Euler's method to calculate the first three approximations to the given initial value problem fo...

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Q: Evaluate the integral. sec (5x + 8) tan (5x + 8) dx

A: ∫ sec5x+8tan5x+8dx

Q: Let f(x, y, z) = 4xy – z² , x = 2r cos(0), y = cos²(0), z = 5r. Use the Chain Rule to calculate the ...

A: Given : f(x,y,z)=4xy-z2, x=2rcos(theta) y=cos2(theta) ,z=5r.

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A: In this question we have to find the deaths by AIDS in 2003.

Q: Use the power reducing formulas to rewrite sin*(2x) without exponents. sin (2x)

A: Given sin⁴(2x)

Q: Let h(x, y) = , x = 41|12, y = 517t2. Use the Chain Rule to calculate the partial derivative. (Use s...

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Q: (x +1)" 2" (n+1)

A:                                                                                        

Q: Evaluate: Jx?cos(2x)dx 2x2sin(2x) – 2xcos(2x) + sin(2x) A + C 4 2x?sin(2x) +2xcos(2x) – sin(2x) В + ...

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Q: Consider the coordinate vectors 6. (w]s= (als= (B]s %3D %3D %3D 3 4. (a) 8)}. w = (?, ?, ?) (b) Find...

A: Solution: b) S = {x2+1,x2 - 1, 2x - 1} and coordinate of q w. r. to s is  {2,0,4}

Q: Activity 3 Find Your Rate at this Moment Directions: Differentiate the following functions and deter...

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Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not un...

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Q: の dy Sーメ+ リーX +5

A: This is a problem related to differential equation. Based on the general formula we will solve the q...

Q: Find dy/dx implicitly and find the largest interval of the form -a < y < a or 0 < y < a such that y ...

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Q: Determine if the given function y = f(x) is a solution of the accompanying differential equation. y'...

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Q: Find the area of the region enclosed by = x2, y = 2x, x = 2, x = -2 %3D Give your answer to the near...

A: The area is given by:A=∫-222x-x2 dx

Q: Determine whether the series converges. >7k-1.01 k=5

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Q: Find the volume of the region bounded by y = x², y = 8x, x = 0, and x 2 rotated around the x-axis. N...

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