1. f(t) = t² – 7 [1,2) 2. g(x) = sin x [0 3. The volume of a cube with sides of length s is given by V = s³. Find the rate of change of the volume to s when s=6 centimeters.

Q: Given that x and y are functions of time, find the indicated rate of change. dy when x 1, y=2, and…

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Q: Can you help me with this problem step by step?

A: The given equation,

Q: Let y = e=/5 Find the differential dy when r = 2 and dæ 0.5 Find the differential dy when z = 2 and…

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Q: Given that x and y are functions of time, find the indicated rate of change. dy dx Find when x= 1, y…

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Q: 9) Where is the function ht) = (t+ 5) differentiable?

A: Given         h(t)= t+51/3

Q: Let y = 5a2. Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4…

A: ∆y = 5(x + ∆x)^2 - 5x^2= 5(x^2 + 2x∆x + ∆x^2) - 5x^2= 5(2x∆x + ∆x^2)= 10x∆x + 5∆x^2 So when x = 4…

Q: (a) Find the differential dy. y = ex/4 dy = (b) Evaluate dy for the given values of x and dx. X = 0,…

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Q: Let y = f(x), where f(x) = Vx + 4. Find the differential of the function. dy =

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Q: (a) Find the differential dy. y = ex/5 dy = (b) Evaluate dy for the given values of x and dx. x = 0,…

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Q: ²+ re" = 2y + e² %3D

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Q: Let y=e^(x/2).Find the differential dy when x=1 and dx=0.3 Find the differential dy when x=1 and…

A: Given function is The differential dy is evaluated as follows,

Q: The Strikers Technologies Company determines that the marginal cost for their MaxiPak flash disks is…

A: We will integrate the function with respect to x and then find the general solution. Next, for…

Q: Given that x and y are functions of time, find the indicated rate of change. dy when x 2 and dt dx…

A: Compute the value of y as follows.Substitute x = 2 in x3 + y3 = 16.

Q: 10) For y=v+8, use the differential dy to approximate Ay when x changes from r=1 to x=0,97

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Q: Let y = 5x?. Find the change in y, Ay when a = 3 and Ax = 0.3 Find the differential dy when x = 3…

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Q: The maximum rate of change of the function f(x,y,z) = x In(yz) at (1;2;) is equal to: V17/2 None of…

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Q: x² (y + z) – 4V/x²+ y² + z² = 0,

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Q: Let y = f(x), where f(x) = X - 6 Find the differential of the function. dy =

A: Diffrential is just put function of y and x separate and then just find f'(x). Now put the value of…

Q: Q5. If W = x² y + 2xyz , x = t², y = t + 1, z = 2t at t = 1. Find the total differential

A: Let's find.

Q: a particle moves along a curve x = t^3+1, y=t^2, z=2t+5 , where t represents the time . its velocity…

A: Velocity is obtained by differentiating the position function

Q: 2. Evaluate dy and Ay if x = 1 and dx = Ax = 1. 3. Find the equation of the tangent line at x = 1.

A: Your question contain only two which i have solved completely.

Q: when

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Q: The volume V of a right circular cylinder of radius r and height h is V = ar?h. (a) How is 4 related…

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Q: Suppose that the position of a body moving along a coordinate line at time t is a. s = a cos kt + b…

A: Part (a):Part (a):Given,Given,

Q: Let y = e/3 Find the differential dy when x = 5 and dx 0.2 Find the differential dy when x 5 and dx…

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Q: 30. Find an equation for the tangent plane to z = f(x, y) at (3, -2) if the differential at (3, -2)…

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Q: H.W: Use the chain rule to find the derivative of w= x² + y² with respect to t dw dt with x = cost +…

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Q: Estimate Ay using differentials. y = x/5 e3x-1 a = 1, dx = 0.1 (Give your answer to four decimal…

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Q: Q2: Suppose the electric potential at (x, y) is given by f(x, y) = 0.5 Ln(x² + y²) estimate the…

A: In this question, we have to find the error in f(x,y) and percent relative error for the given value…

Q: Given that x and y are functions of time, find the indicated rate of change. dy when x 4 and dt dx…

A: First obtain the derivative of the given equation as follows.

Q: (a) Find the differential dy. y = eX/5 dy = 4 (b) Evaluate dy for the given values of x and dx. x =…

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Q: b) Find the value of the derivative of f(x, y, z) = xy + yz + xz with respect to t on the curve x =…

A: There are two methods to do this: One is direct method which we used and other is by chain rule.

Q: ) L(3.98) where L(x) is the linearization of y = √√x +3 at x = 1 (tangent line approximation)

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Q: Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4 and dæ = 0.4

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Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: If x*y+2x+z°=1 find the rate at which z is changing with respect to x at the point (2/5,2/3,1/3)

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Q: 51. grad f = (2x + 3e")7 +3xe'j

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Q: Step 3 The total differential dz for the function z = x?y is dz = ydx + dy.

A: We need to find dz.

Q: at is the maximum rate of change of f (x, y,z) at P?

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Q: are

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Q: Can i get help step by step?

A: We take ln on both sides and use logarithmic differentiation. Using the product rule and power rule…

Q: Given that x and y are functions of time, find the indicated rate of change. iON dx dy = 2, given…

A: Consider the given equation

Q: Given y = V4x+5, find the differential dy when x = 7 and dx = 0.3. Round your answer to three…

A: Take derivative with respect to x and put the given values.

Q: (a) Find the differential dy. y = ex/4 dy =| (b) Evaluate dy for the given values of x and dx. x =…

A: Given y = ex4(a) we find the ditterential d y(b) Evaluate d y for the given values of x  and dx…

Q: Show that a particle, located at the origin at t = 1 and moving along the x-axis with velocity v(t)…

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Q: Given y = = V4x + 5, find the differential dy when.x 7 and dx = 0.3. Round your answer to three…

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Q: (a) Find the differential dy. y = eX/2 dy = (b) Evaluate dy for the given values of x and dx. X = 0.…

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