x, F(x) = f(t) dt Jo

Q: Let f(x, y) = sin(x+ y²). Compute the rate of change in the direction of fastest decrease for f at…

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Q: Find the indicated partial derivative f(x,y,z) = x2cos(yz),     fxzy

A: Consider the function  fx,y,z=x2cosyz

Q: Use order of h® Romberg integration to evaluate xe2x dx

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Q: Suppose a force of 40N is required to stretch and hold a spring 0.1m from its equilibrium position.…

A:

Q: Find the indicated partial derivative. f(r, y, :) = e"vz*; fzyz fxyz(x, Y, z) =

A: Given: f(x,y,z)=exyz3 To find: fxyz=?   Required formulas: Power rule: ddxxn=nxn-1 Product rule:…

Q: Find partial derivative føyz of the function f(x, Y, z) = z ln x + 2y

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Q: Differentiate implicitly to find the first partial derivatives of z                              xz2…

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Q: 19) Derive a one point integration formula to estimate the integral f (x) dx.

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Q: Find all second order partial derivative with respect to variable x and y. F(x,y)= x cosxy + y sinx…

A: We have to find all second order partial derivative with respect to variable x and y: Given:

Q: a?f (or and y. that is, f(x,y) = e² with respect to ayax axay Calculate the second-order partial…

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Q: Find the second partial derivative of the function f(z, y, z) = 2°yz+ at the point (1, 1, 1). yz

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Q: Compute the derivative: 3 | Vsin t dt dx

A: To find ddx∫x3sin t dt We know that, ddx∫u(x)v(x)f(t) dt = f(v(x))v'(x)-f(u(x))u'(x) Then, we have,…

Q: Find the partial derivative f(x,y) = x7y fx(x,y) = ? fy(x,y) = ?

A: The given function is: f(x,y)=x7y

Q: Find the partial derivative at point(u,v)=(-4,0) of w=ln(xa+yb+za),x=uevsin u y=uevcos u, z=uev,…

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Q: Find the third derivative of ƒ (z) = VT2z+I. f" (z) =

A: We use the exponent rule and chain rule.

Q: Find both first partial derivatives. . z = ln x/ y

A: Given that z=lnxy

Q: Find the maximum rate of change of f (x, y) = xy ^ 2 + root (y) at the point (2,1). in which…

A: The maximum rate of change of f(x, y) happens along the direction grad(f) at the given point (2, 1).…

Q: Use differentials to approximate the increase in the area of a soap bubble when its volume increases…

A: Let the radius of the soap bubble be a cm, then the volume of the soap bubble is: V=43πr3        And…

Q: Verify the power rule for integration fx'dx= n+1

A: Given a power rule of integration,

Q: Compute the indicated partial derivative. 5x g(x, y) = x + 2y a?g ду? =

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Q: Find the set of orthogonal trajectories for r = VA sin (2e)

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Q: Find the Integration of: f(3sin t + esin ty cost dt In 3

A: we have to integrate the following

Q: Compute the partial derivative: f(x, y) = sin(x" –- 3y) fy(0, ) =

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Q: Find the first order partial derivative with respect to y S(x, y) = a"y² + 3ze"

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Q: Differentiate implicitly to find the first partial derivatives of w                            w −…

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Q: find the first partial derivative  f(x,y) = squareroot (2x+y^2)

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Q: ompute the partial derivative: (1, y) = cos(x+ – 6y) -(0, т) —

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Q: Find F '(x). F(x) = integral of 2/(x+8) dt in interval [x^2,0]

A: Let u=x^2 Then du/dx=2x

Q: 2. Given that y= -- Use a limit to find the instantaneous rate of change of y with respect to x at…

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Q: Compute the derivative of f (x, y) = (y + 2) + xysin(x) at (0,1).

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Q: Use the second partial derivative test to find the relative extrema of f(x,y) = -x³ + 4xy 2y2 + 1.

A: The given function is  f(x, y)=-x3+4xy-2y2+1

Q: Differentiate implicitly to find the first partial derivatives of z. x + sin(y + z) = 0 az Əx az dy…

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Q: Use order of h8 Romberg integration to evaluate xe2x dx

A: Let us start solving and find et value

Q: Does the differential dy represent the change in f or the change inthe linear approximation to f ?…

A: Given the differential is dy.

Q: Find the second-order partial derivative fxx ( x , y ) of the function f ( x , y ) = x 4 y 4 - sqrt…

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Q: Differentiate the accumulation function F(x)= [ In(t)dt. HINT: Chain rule.

A: Topic = Derivative

Q: Find using the appropriate Chain Rule for W =y- 7x*y where x = e° and y = e", and evaluate the…

A: The given function is w=y3-7x2y where x=es and y=et. Differentiate the function w=y3-7x2y partially…

Q: (b) Use differentials to estimate the maximum error in the calculated volume. What is the relative…

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Q: Evaluate the fallowing de fiñi te integril (x+) dx

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Q: Find both first partial derivative h(x, y) = e-(xª + y^) hx(x, y) = hy(x, y)

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Q: (d) Compute the driectional derivative of f at (1,2) in the direc- tion u = (e) • point (1, 2)? What…

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Q: Find partial derivative of: z=f(x,y)= e^x^2+y^2  +   cos(x+y^2

A: For this question of partial derivative we need to find out first derivative with respect to x and y…

Q: : Evaluate fxe dx to using Romberg integration to an error of order

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Q: but its partial derivatives are not continuous at (0,0).

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Q: Find the derivative of g(x) = |. •r In z Vt2 +t+1 dt

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Q: ar Let = 2x - 1. Integrate this partial derivative with respect to x, letting h(y) be an unknown…

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Q: (or axay дудх Calculate the second-order partial derivative of f(x.v) = xy with respect to x and y,…

A: Given  f(x,y)=xy

Q: Find the first partial derivatives of the function. f(x, у) : cos(t5) dt fx(x, y) = fy(x, y) =

A: We use the leibniz derivative.