Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with the value obtained using a calculator.

Q: Find the directional derivative of z = f (x, y) = x²y³ – 3y² at (-3,4) in the direction of the…

A: Use directional derivative formula which is mentioned in solution.

Q: Let y = 3x + 2x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

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Q: Find the derivative of y with respect to t. 10t y3Dcsc dy %3D dt

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Q: Let y = sin(3x). If Ax = 0.4 at x = 0, use linear approximation to estimate Ay Ay ~ = 1.2 Find the…

A: Use the following formulae, to obtain the solution. ∆y=fx+∆x-fxdy=f'xdxError…

Q: Use the chain rule to find the derivative of w= x + y with dw with x cost + sint, y= cost– sint dt…

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Q: Where f(x, y) y calculate (–1, 1) towards the point dv (-1, 3)

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Q: IND THE ORTHOGONAL TRAJECTORIES OF THECURVES Y =Cx²,WHERE CIS AN ARBITRARY CONSTANT.

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Q: z = Vx4 + yf, fz (1, 2)

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Q: use Separation of Variables to find the general solution. dy/dt= y tan t

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Q: integrate ƒ over the given curve. ƒ(x, y) = x3>y, C: y = x2/2, 0 <=x<= 2.

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Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

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Q: Let y 5x + 6x + 2. If Ax = 0.2 at x = 1, use linear approximation to estimate AY Ay =

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Q: 4. Use the contour integration to find f G dx. 1 x4+16

A: Answer: π/(16√2)

Q: Let y = sin(5x). If Ax = 0.4 at x = 0, use linear approximation to estimate Ay Δy ~ Find the…

A: Given: y=sin(5x) ∆x=0.4  at x=0   Solution: y=sin(5x) For the function y=f(x),   ∆y=f(x+∆x)-f(x)…

Q: Let y = sin(2x). If AI = 0.3 at x = 0, use linear approximation to estimate Ay %3D %3D Ay = %3D Find…

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Q: Why does this work? If we have the curve in the xy-plane: F (x, y) = 0, then why is the implicit…

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Q: Let y = sin(5x). If Ax : = Ay ~ = Find the percentage error error = 0.2 at x = 0, use linear…

A: Linear approximation of y=f(x) at x=x0 is L(x)≈f(x0)+f'(x0)(x-x0)

Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: Let y=sin(2x). If Δx=0.4 at x=0, use linear approximation to estimate Δy.

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Q: 2. Find the equation of the tangent plane to f(x,y) = sin(x² +y) when x = 0, y = T. 3 and r - cost

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Q: By using the definition of the derivative, use a clear diagram to argue that d S(t)dt = f(x). %3D dx…

A: We have to prove that ddx∫axftdt=fx This will be prove by Newton's Leibnitz rule in this rule we…

Q: In what direction is the derivative of ƒ(x, y) = xy + y2 at P(3, 2) equal to zero?

A: Consider the function and solve.

Q: Find dydx? for f(x, y) = eXy

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Q: In what direction is the derivative of ​f(x,y)=xy+y^2 at ​P(5​,4) equal to​ zero?

A: Given,

Q: Find the slope of the tangent line to the curve y = x e× at (2.5,2.5 e 2.5). dy (2.5,2.5 e 2.5) dx…

A: We know that slope of a line is defined by , m=dydx. Therefore, we need to take the derivative of…

Q: Let y sin(3x). If Ax = 0.2 at x = 0, use linear approximation to estimate Ay Ay 2 Preview Find the…

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Q: : Find the derivative of f(y, z) = ze2y + cos(2zy) at ppoint (9,1,0)in the direction of V = 2i – 3j…

A: This is directional derivative, just write the formula and solve accordingly.

Q: Find the total differential. z = 2x6y9 dz

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Q: Find the derivative of the function. -1 y = (3t – 1)(6t – 5) dy dt II

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Q: Let y = 5x + 3x + 4. If Ax = 0.1 at x = 5, use linear approximation to estimate Ay Ay =

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Q: What is the derivative of f(x,y) y° at P = (3, 1) in the direction toward %3D Q = (4, –3)?

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Q: The derivative of f(x,y)=9xY at (e,1) in the direction of v=(4,3) is !!

A: TO FIND THE DERIVATIVE i.e DIRECTIONAL DERIVATIVE IN DIRECTION OF V= (4,3) at (e,1) STEPS 1. FIRST…

Q: Let y = sin(4x). If Ax = 0.1 at x = 0, use linear approximation to estimate Ay Ay = = Find the…

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Q: Let y 3x + 4x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

A: Given, y=f(x)=3x2+4x+4 ,∆x=0.4 at x=1 Differentiate with respect to x, we get f'(x)=6x+4 At point…

Q: Find the derivative of y with respect to t y = In (t2) dy %3D dt

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Q: The directional derivative of f(x, y) = -e" cos y at (0, ) in the direction of v = (-6,8) is

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Q: Let y = sin(4x). If Ax 0.4 at z 0, use linear approximation to estimate Ay Ay 2 - Find the…

A: Solution :-

Q: Find the point of intersection of the tangent line to v=sin(2r) at y=0 and the line %3D x+2y=5.

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Q: Let y = sin(5x). If Ar = 0.4 at r = 0, use linear approximation to estimate Ay Ay 2 %3D Find the…

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Q: Let y=sin(4x).If Δx=0.2 at x=0, use linear approximation to estimate ΔyΔy≈   Find the percentage…

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Q: The directional derivative of f(x, y) = e" cos Y at (0, ) in the direction of v = (-6, 8) is

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Q: aw nd dt in term of t, if w = xy, x = cost and y = sint, when t = - %3D

A: Question 4 is not complete.  I am answering Question 5.

Q: Let y sin(2x). If Ax = 0.2 at x = 0, use linear approximation to estimate AY Ay z = Find the…

A: given: y=sin2x∆x=0.2x=0 as we know that, ∆y=dydx∆x dydx=cos2x2=2cos2x

Q: In what directions is the derivative of f(x,y) = xy + y at P(8,5) equal to zero?

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Q: dy Compute the derivative y' dt 2t – 9 - y = 5t 2

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Q: The directional derivative of f(x, y) = e" cos y at (0, ) in the direction of v = (-6,8) is

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Q: Use the Trapezoidal Rule with n = 4 to estimate f, x² dx. Compare the estimate with the exact value.

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