The acceleration function (in m/s2) and initial velocity for a particle moving along a line is given by 9t36, U(0) 45, 0

Q: Determine the instantaneous rate of change of the function πt ³ √x sin 2 f(x) = LV x3 1 + √t at x=2.…

A: Leibnitz integral rule.

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

A:

Q: If (x, y) moves from (x0, y0) to a point (x0 + dx, y0 + dy) nearby, how can you estimate the…

A: The resulting change in function f (x, y) is given as:

Q: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

Q: A particle moves along the curve y = x^(3/2) in the first quadrant in such a way that its distance…

A: Let (x,y) is a point on y = x^(3/2)Distance of (x,y) from (0,0) is given by:

Q: Find partial derivative af dx for the function f(x,y) given below exp 2x. siny .(at the point (In2,…

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Q: x tan(yz) ey – 4x3z2 3: Find the total derivative of f(x, y, z) =

A:

Q: Another particle has a velocity function of v(t) = [' 2'-* dx. What is the acceleration of this…

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Q: 3. (D - 3D? + 4)y = 40cos2x + 6

A:

Q: Find the total differential. z = 5x3y9 dz =

A:

Q: If the acceleration of a particle is given by ä = sint i+ cost +e k, find the relity and position…

A: The acceleration of a particle is…

Q: The dimension of a box are b, b + 1, b + 4 . Find how fast the total surface area A increases as b…

A: Given that sides of box Length L=b Height h=b+1 Width w=b+4

Q: Use differential to approximate the change in y=x3+x2 as x changes from 1 to 0,95.

A:

Q: Find the maximum rate of change of the function f(x,y) = sin (xy) at the point (4,0) and the…

A: The given function is f(x,y)=sin (xy) and the point is (4,0)=(a, b). to find : Maximum rate of…

Q: Consider the function f(x, y) = y³ – 2y – x². Find the direc- tion of greatest increase at the point…

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Q: Determine the average rate of change of the function y = sinx from X = 0 to x = 2 O1 2

A: The average rate of change of the function f(x) can be calculated using the formula Average rate of…

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

A: We use the exponent rule and chain rule.

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: Find the most general antiderivative of f(x) = -3e" + 10 sec2 (x), where - < x < 2 Note: Any…

A: According to the given information it is required to calculate the antiderivative of the function:

Q: A particle moving along the x-axis has velocity function v(t) = t sin t. How far does the particle…

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Q: Find partial derivative of dx for the function f(x.y) given below exp 2x. siny .(at the point (In2,…

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Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: Economists have considered the output y of a manufacturing process as a function of the size of the…

A: The output of a manufacturing process as a function of the size of the labor is given as follows.…

Q: A particle moves along the x-axis with velocity dx/dt = ƒ(x). Show that the particle’s acceleration…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occur f(x, y)…

A: Topic- Vectro

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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

A: Find gradient and its magnitude then solve

Q: Use linear approximation (or differentials) to estimate the given number. 3 а. V8.12

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the derivative of the function f(x, y) = e³ at the point (0, 2) in the direction in which the…

A: The derivative of function f(x,y) can be determined by the gradient of the function,…

Q: Find the first-order partial derivative with respect to x of f(x,y) = e5x siny.

A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

Q: .A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Using double derivative test to get max value of x

Q: The average rate of change of the function y = x² in the interval 2 sx< 5 is %3D

A:

Q: Determine the instantaneous rate of change of the function f(x) = [x² si sin (2¹) 1+√t x3 At x=1 dt

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Q: B: Use the Chain Rule to find the derivative of f(x,y) xy with respect to (t) along the path y =…

A: Solution:-

Q: A particle moves along the curve y= /1+x³. As it reaches the point (2, 3), the x-coordinate is…

A: NOTE: Refresh your page if you can't see any equations. . the given point is (2,3) so x=2 and y=3…

Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

A:

Q: ue of J. Note that the lows

A: Given ∇.V=1r2∂∂rr2vr+1rsinθ∂θ∂∂θsinθvθ+1rsinθ∂vϕ∂ϕ

Q: Assume that all variables are implicit functions of time t. Find the indicated rate. x2 + 8y2 = 33,…

A: Explanation of the answer is as follows

Q: Find the total differential dw. 5. w = x tan¬ y – 2ªyz

A: The objective is to find total derivative dw.

Q: A total cost function (in dollars) is given by C(x) = 116 + 3x + 0.37x. Use differentials to…

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Q: . Use a similar procedure to estimate the instantaneous rate of change of y = 3" at r = 0. Show your…

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

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, y)…

A: First find gradient and take magnitude for max rate of change

Q: B: Use the Chain Rule to find the derivative of f(x,y) = xy with respect to (t) along the path y =…

A:

Q: Find differential of the function y = (x² + 3)°. dy = dx. When x = 4 and dx 0.05, compute the…

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Q: Find the total differential. z = 10x y10 dz =

A: As we know that the: If the given function is z=fx,y then the expression for the total differential…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x,…

A: SOLUTION-

Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

A:

Q: A curve y = /(x) have length of the curve from x 0 to x= n/2. dy Vcos(2x - 2) as its first…

A: