O ди If u = f(x,y), x = g(w) and y = h(w), using Chain Rule, what is aw O ди aw ди Əw || O all of these ди дw || || du du Əи (ax) + Ən (dx) ax dw ду \dw du (dx dx dw. ?u /дх ?х дw + + du (dy dy dw ди (ду ду h ?

Q: If f is a differentiable function and % up on Selected Answers: (0,1) f'(x)=x5 − 5x4+ 5x³+2, then…

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Q: Find dw/dt using the appropriate Chain Rule. Function w = x² + y² x = 4t, y = 5t dw dt || Value t =…

A: Given: w=x2+y2, x=4t, y=5t and t=2.   Apply the Chain Rule; dwdt=∂w∂x·dxdt+∂w∂y·dydt    ...1

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Q: 6 (2) Find and draw the Fourier transform of f(t) = 9+t²

A: Find and draw the Fourier transform of f(t)= 6/(9+t^2)

Q: Integrate I -dz Select one: O A In 1-¹-2²+√1 − x² + C I OB. 21n1-¹³+√1 − x² + C | OC. In 1-²+√1 = z²…

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Q: Get the interval and radius of conv this given power series (x - 3)" n

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Q: Determine the general solution of the differential equation

A: Follow the procedure given below.

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A: Solution of given question is written in below steps.

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A: Here we have to find the limits and then state whether it diverges or not.

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A: Here we have to find the directional derivative.

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A: To find the minimum distance from a point to a paraboloid is just to minimize the function…

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Q: a) Find an equation of the tangent plane to the surface at the given point. xyz = 15, (1, 3, 5) b)…

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Q: 1. y (4x + y) dx -2(x²-y)dy = 0 2. (2xy4e + 2xy³ + y)dx + (x²y4ey - x²y²-3x)dy = 0

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Q: 1. Find the Taylor polynomial p3 centered at a = 7/3 for f(x) = = COS I.

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A: We need to choose correct option.

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A: Given equation of hyperbola (x-2)29-(y+4)216=1That is (x-2)232-(y-(-4))242=1copare with…

Q: Solution is incorrect. Please correct it.

A: dydx=6y18+9x2y18⇒dydx=6y18(1+9x2)⇒y18dy=6(1+9x2)dx

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Q: f(x, y) = x²y + 4y and x = st, y = 2t - 3s. af and off. af Use Chain Rule to find ds Write your…

A: Follow the procedure given below.

Q: 2. Suppose that f (x, y), g(x, y) are two continuous functions on the xy plane. Is it true that So…

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Q: To evaluate the integral I cos cos4 x sin3 xdx we save one sine factor and use sin² x = 1 cos²x to…

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Q: Find lim f(x) if I-00 4x - 1 I 5.

A: NOTE: Refresh your page if you can't see any equations. . here we have

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Q: Identify the surface represented by equation: 9x^2 + y^2 - z^2 + 2z -10=0

A: Given :9x2+y2-z2+2z-10=0

Q: 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1,-1).

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Q: Sdr Select one: O A. OB. O C. O D. (2x-1)³ V + √2x−1+C 3 +√√2r-1+C +√√2r-1+C + √√√2r-1+C (2z-1)³…

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Q: S cscycoty 1+cacy dy Select one: OA. - In (1+ csc y) + C OB. In (1+ csc y) + C OC. In² (1+ csc y) +…

A: Given problem:-

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A: NOTE: Refresh your page if you can't see any equations. . compare this DE with  so here we have…

Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

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Q: The limit: x - y lim (x,y)→(0,0) x² + y² exists, and equal to 0 Select one: O True O False

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Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. an = tan…

A: The given sequence,   an=tan-1n

Q: Use the Ratio Test to determine whether the series is convergent or divergent. (-1)^-1_57 47n3 n = 1…

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Q: Solve the initial value problem: dy dz 9y, y(0) = 1

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Q: tan² (x) sec¹(x) dx.

A: Given, ∫tan2(x)sec4(x)dx

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Q: Find the solution of the following IVP: y(t) = = dy dt 2ty=9t²e, y(0) = 5.

A: We have to solve the given IVP.

Q: If f(x, y, z)=√x²y² z², then fxyz (x, y, z) = 2xyz √x² 1² z² Select one: True O False

A: We have to state if given statement is true or false.

Q: Find the derivative of y = arccos x + x 1-x²

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Q: The partial derivative with respect to x of the function f(x, y) = x²y + cos y + y sin x ? Select…

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