Consider the following equations. y = x, y=x²

Q: 2. Use integration in cylindrical coordinates in order to compute the vol- ume of: U = {(x, y, z) :…

A: We have to use cylindrical coordinates in order to find the volume of thegiven region.

Q: Two circles have the same center. The inner circle has radius r which is increasing at a rate of 3…

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Q: Consider the function f(x,y)=e^4x−x^2−4y−y^2. Find and classify all critical points of the…

A: Given function:- fx,y=e4x−x2−4y−y2

Q: Evaluate the given integral by changing to polar coordinates. 160-x²-1² dA, where D is the region…

A: Consider the provided question, We need to evaluate the integral  ∬De-x2-y2dA by changing to polar…

Q: The Third Gate You arrive at the third gate and look for the inscription. Your computer translates…

A: Given: Limits include an arbitary real number, c.Find the limits limx→c+33(x-c)2 and limx→c-33(x-c)2

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=2-2².…

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Q: A particle moves according to a law of motion s = f(t), t≥ 0, where t is measured in seconds and s…

A: Note:- These are multiple subparts question and we can solve maximum 3 sub parts. So i am solving…

Q: 5. If 3x²z+y³-xyz³ = 0, find az / əx. 6. Show that if w=f(r-s,s-t,t-r), then dw dw dw dr + + = ds ôt…

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Q: Find the general solution of the following reducible second-order differential equation. Assume x, y…

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: Some value of f(x) and f'(x) are given in the table. If no value is given, then you should assume…

A: Given Table:- x 4 5 6 f(x)   -3   f'(x) 1 ϕ 1

Q: A volume is described as follows: 1. the base is the region bounded by x = -y² +12y +7 and x = y² −…

A: Given that x=-y2+12y+7 and x=y2-24y+151we have to find volume of object

Q: A warehouse selling cement has to decide how often and in what quantities to reorder. It is cheaper,…

A: The given data is: C=5aq+3bq

Q: Consider the functions graphed below. C (0,b) (1,1) (a) Find the slope of the line. slope = Answer…

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Q: If f(7) = 7 and f'(7) = 4, estimate f(6.7). f(6.7)~

A: f(7)=7f'(7)=4from leanear approximation f(x)=f(a)+f'(a)(x-a)

Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

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Q: Let a = (4, 0, 5) and 6 = ( − 3, − 1, 1). - Find the projection of b onto a. projā b = < Calculator…

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Q: Determine if the limit lim (1+5x) 1+0+ exists, and if it does, find its value.

A: Given: limx→0+1+5x12x

Q: y' = xy³ (1 + x²)−¹/2, y (0) = 1

A: y'=xy3(1+x2)-12  dydx=xy3(1+x2)-12given  y(0)=1∫xndx=xn+1n+1+c

Q: After walking through the fifth gate, your computer informs you that more than half of the gates…

A: Given function f( t ) = 1a( 2t3 - 15t2 + 45 )

Q: Consider the function g(t) = = t 7+t²

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Q: What is the x-value and y-value of the point of intersection of y=-3x+10 and y=2x-5?

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Q: lim 5x³ +16x²-10 12x3+x+28

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Q: Use linear approximation to estimate the value of the following  cos(pi/4 +0.01)

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Q: Use f(x) = x - bln(x) to answer the questions below. Assume b is a positive constant and x > 0. (a)…

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Q: Evaluate the double integral 10. Answer: 10ry dA, where D is the triangular region with vertices (0,…

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Q: 1) Find the radius of convergence for f(x) =(-1)^4+1 ²n+1 n=0 4n+2

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Q: Find the derivate of the functions of at any Use the form f'(c) = lim f(x) - f (c) for a and b X->(…

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Q: The differentiable functions f and g are defined for all real numbers x. Values of f, f, g, and g'…

A: Derivative

Q: Solve the separable differential equation dx 1 x² + 25 dt and find the particular solution…

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Q: Use logarithmic differentiation to find the derivative of the function. y = (tan(x)) 5/x y' =

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Q: Verify that the given differential equation is exact; then solve it. (21x²y³ + 4y) dx + (21x³y² + 4y…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as a…

Q: let y = 5 log (x+1) find y'

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Q: Consider the ellipse 9x² + 64y² = 576. Consider the point P(16,3). Find an equation for both lines…

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Q: Find the cross product a x b. a =j + 6k, b = 5i - j + 4k Verify that it is orthogonal to both a and…

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Q: Suppose that f(x) = x³ - 6x² + 15. (A) List the values of all local maxima of f. If there are no…

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Q: Find the general solution to the given differential equation. (Remember the constant of…

A: To find general solution of differential equation As per our guidelines we are supposed to answer?️…

Q: A lamina with constant density p(x, y) = p occupies the given region. Find the moments of inertia Ix…

A: Solution is given below:

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Q: 2. Determine whether the series is convergent or divergent. If it is convergent, find its sum. ܐ 5…

A: The Series ∑n=0∞arn is called geometric series and the geometric series a is the first term and r is…

Q: Verify that the given differential equation is exact, then solve it. 10x 24y 16y 5x (3) dx + X y 4 X…

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Q: 3. Evaluate the limit, if it exists: lim a. 0 b. 7 x² + x + 1 x+2 X²-2 c. 3.5 d. does not ex

A: H=limx→2x2+x+1x2-2

Q: Consider the ellipse 4x² + 2xy + 2y² = 88. (a) The derivative on this curve is dr dy = dx (b) Find…

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Q: Some rational functions can have both horizontal and vertical asymptotes.  Suppose that you have a…

A: Solution for above requirement are as explained below.

Q: Consider the function f(0) = 7sin²0 - 7cos0. (a) Find f'(0) = 7 sin (20) + 7 sin (0) (b) Find the…

A: f(θ)=7sin2(θ)-7cosθ(i)  d dθ(sinθ)=cosθd dθ(cosθ)=-sinθ

Q: Consider the following planes. -5x + y + z = 5 15x - 3y + 5z = 25 (a) Find the angle between the two…

A: Consider the following planes -5x+y+z=515x-3y+5z=25a To find the angle between the two planes.b To…

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y=x and y=2-x…

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Q: Compute [5t³ - 8t + 1] d dt

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Q: Solve the equation for the indicated variable. R1 R2 for R₂ R₂ X

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Q: Determine the slope of tht line through the given points. (-7,-1) and (-5,9)

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Q: 2. Find the area of the region between two concentric circles r =7 and r=10

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