Suppose z = x² sin y, x = −5s² + 3t², y = -6st. A. Use the chain rule to find 53 33 and as functions of x, y, s and t. B. Find the numerical values of and when (s, t) = (-2,-2). (-2,-2)= (-2,-2) =

Q: Particle Motion from Equation (Level 2) Oct 22, 11:44:25 PM A particle moves along the x-axis so…

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Q: e + ey (x,y) (0,0) cos x + sin y Evaluate the general limit lim

A: L=lim(x,y)→(0,0)ex+eycosx+siny Since the limit to be found is as x  y approaches 0, substitute x=0…

Q: dy dx x5(x + y) = y²(6x - y) X

A: Topic - application of derivatives

Q: Given the polynomial y = 3x³ +21x² +31x + 2, • list the possible rational roots: 2 2 1,-1,-1,- 2,-2,…

A: The given polynomial y=3x3+21x2+31x+2 We have to find the all possible rational roots of the…

Q: Find fx and fy, and evaluate each at the given point. arctan(ỵ), (2,-2) f(x, y) fx(x, y) = fy(x, y)…

A: Given:        fx,y=arctanyx , 2,-2     fxx,y=∂∂xarctanyx                   =1yx2+1∂∂xyx taking y as…

Q: O-11 60

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Q: Suppose that a population develops according to the logistic equation dP dt = 0.06P − 0.0006P2,…

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Q: If two integers have opposite parity, then their product is even. Direct proof.

A: Topic = Algebra

Q: To which of the following will lim x+1 lim x-1X+4 x+1 lim x-1X+3 x+1 lim *4-1X+2 x+1 (x + 1)²…

A: Given, limx→ -1x+12x+22-1

Q: Find the inverse Laplace transform L-¹{F(s)} of the given function. 12 s² + 16 Your answer should be…

A: To find the inverse Laplace transform L-1Fs of the given function.Fs=12s2+16

Q: 2x +3 x²-9 da

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Q: (x - 1) If 1 / ² ) = = √ Ada² + √ dx [ B (x − 3)(x + 7) - 3 - then A+B = Bdx x +7'

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Q: Find the surface area generated by rotating the given curve about the y-axis. x= 3t²2², y = 2t³, X=…

A: The given curves are  x=3t2, y=2t3,    0≤t≤1

Q: Consider the function f(x) 72x² + 10, The absolute maximum of f(x) (on the given interval) is at X =…

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Q: 2-x 2 +5 1 dx

A: Given, ∫2-xx2+5xdx

Q: Find the derivative of the following function. x cos ¹1¹(7x) O O о O 7x √₁ 1 – 49x² 7x √1 − 49x² -7x…

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Q: A company that produces cell phones has a cost function of C = 5x² - 155x + 6619, where C is the…

A: Given query is to find the number of units need to be produced to minimise the cost.

Q: (5+51)³

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Q: ← The following table gives the monthly premiums for an insurance policy on people of various ages.…

A: The given data is: age monthly premium       35 127       40 164       45 242       50…

Q: Find the linear approximation at x = 0 to show that the following commonly used approximations are…

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Q: Find all second-order partial derivatives for the function r = In |5x+y|. XX xy 11 = 25 (5x + y)²

A: Given function:- r=ln5x+y

Q: Find the first partial derivatives of x - y x+y f(x, y) = af -(1, 1) = д х of ду -(1, 1) = = at the…

A: Concept: Let's say we have a function f(x, y) that depends on the values of two independent…

Q: er Derivatives 2.) What is d² y dx² Period when y=cos(2x³)

A: 4) The given function is; f(x)=lnx, x=3.

Q: Consider the function f(x) = 1 − 6x², − 5 ≤ x ≤ 2. The absolute maximum value is and this occurs at…

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Q: Find the absolute maximum and absolute minimum of the function f(x) = -2 sin² (x) over the interval…

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Q: x³ Find the absolute maximum and absolute minimum of the function f(x) = - 4x² + 12x - 5 over the…

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Q: Evaluate the integral R --²dA where R is the region bounded by the semicircle z = √4-y² and the axis…

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Q: The composite function theorem allows for the demonstration of which of the following statements? O…

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Q: O 62 sin² (1) da = In(sin(x)) + 6 In(sin(x)) In(sin(x)) + In(sin(x)) (Apply integration by parts…

A: ∫u(x)v(x)dx=u∫v(x)dx-∫ddxu(x)∫v(x)dxdx ∫cotxdx=ln|sinx| ∫csc2xdx=-cotx

Q: Le symbole sigma pour la somme est une notation standard en mathématiques qui nous permet d'exprimer…

A: Given information (a):-   ∑i=1n f(x1),     (b):-  ∑i=1n f(xi), (c):- ∑i=0n xi ,           (d):-…

Q: A farmer finds that if she plants 100 trees per acre, each tree will yield 45 bushels of fruit. She…

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Q: du Evaluate at (x,y,z)=(4,3,0) for the function u(p,q,r) = e Pacos(r); p = = = ²1/₁, q=x² Iny, r=z.…

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Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=4f(x)+5x. If the…

A: Given: the derivative of the function, f'x=4fx+5x

Q: 3 [(1 + 5a)'di

A: Solve the integral

Q: A rectangular box has a width of 7 cm and a length of 1 cm. The volume of the box is decreasing at a…

A: Topic = Volume

Q: Determine the area of the region bounded by two the curves f(x) = 2²-26z+72 and g(x)= 13z +36.

A: To find the area of the region bounded by the two curves.

Q: The area of the region bounded by the two curves y = x² and y = 16 is Square Units

A: To determine the area of the region bounded by the two curves y=x2 and y=16.

Q: Determine the area of the region bounded by two the curves f(x) = x² – 22x + 48 and g(x) = 11x + 24.

A: Topic = Area

Q: The area of the region bounded by the two curves y = x² and y = 81 is. Square Units

A: Topic = Area

Q: Evaluate the following definite integral leaving the result in its EXACT form by showing the…

A: Given integral:- ∫0π3sinxlncosxdx

Q: A baseball team plays in a stadium that holds 50000 spectators. With the ticket price at $8 the…

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Q: A helicopter starting on the ground is rising directly into the air at a rate of 21 feet per second.…

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Q: 200 2. Evaluate: 22oo(2x – 5)2

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Q: Find the derivative of the function. 14 logg(t) t g' (t) = g(t) =

A: Topic = Derivative

Q: nd a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Let f(x) = x( 1 — [1]) and g(x) be any function. Prove by epsilon-delta definition that lim g(f(x))…

A: Limit

Q: Given the graph of f(x), which value is the f(6)-f(5) least: f(5), f'(5), or ? 6-5 -2 f(5) f'(5) 50-…

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Q: If y=xe, then find d" y dx"

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Q: Let s(t) v(t) = = 4t³ + 42t² + 144t be the equation of motion for a particle. Find a function for…

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Q: wo yeast populations are grown in a lab on campus. The first population grows according the DDS…

A: NOTE: Refresh your page if you can't see any equations. . the first population grows according to…