Find the function r that satisfies the given condition. r'(t) = (5, sin 8t, sec ct); r(0) = (3,3,3) r(t) = (OOD %3D

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: topic - derivative of a function

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Q: Find for the following function: dx 1- y = sin-1 V2x + 3 2- y = 3cot(cosx) 3- y = x*y at x = 1

A: We have to find the derivative of the following functions.

Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: Find the differential of each function. (a) y = tan(7t) dy = 3 - v2 (b) у 3 3 + v2 dy =

A: topic - differential equations

Q: Let f(x, y) = sin(3x + 5y) and P = 3 Find the maximum rate of change of the fucntion f at the point…

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Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

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A:

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: If y= sin f dt, then dy is dx 2x sin x sin x 2 VX sinx 2x sinx

A:

Q: The linear approximation at x = 0 to sin(9x) is A + Bx where A is: and where B is:

A: Given fx=sin9x Differentiate fx=sin9x with respect to x, we get f'x=ddxsin9x=9cos9x Hence,…

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A: Given function:

Q: The integrating factor of the LDE y'=x-2ycotx is A B с D sin²x sec²x csc²x cos²x

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Q: Find aw/as and ôw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) X = s + t, y…

A: we have to find partial derivative by using chain rule

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A: Given:

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Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: and where B is:

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Q: Let y = tan(3x + 6). Find the differential dy when x = 2 and dæ 0.2 Find the differential dy when x…

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Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

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Q: 2. Find the length of the curve: y = 2 In (sin (x)):sxS*

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Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

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A: This is a problem of linear approximation.

Q: tan st e dt 2

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

Q: a(22) V17 – cos(2nt)" (2 – 4) sin() 1. Given f(x) dt, find the equation of the line tangent to the…

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Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: Find the equation of the tangent line to the graph of F(r)= 2z²+2r+1 evi dy at r 0. sech z

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Q: Q3: Find if: dx 2x dt sinx dt (1) y = (2) y = [ %3D t- 2 X cosx

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Q: se the Chain Rule to find dw/dt. w = INVX2 + y2 + z² x = 9 sin(t

A: Here we have to use the chain rule to find dwdt=? w=lnx2+y2+z2, x=9sin(t), y=3cos(t), z=5tan(t)

Q: The linear approximation at x = 0 to sin (7x) is A + Bx where A is: and where B is:

A:

Q: The distance between two moving objects whose positions are given by ( x₁, y₁ ) and ( x₂, y₂ ) is…

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Q: The linear approximation at x = 0 to sin(6x) is A + Bx where A is: Preview and where B is: Preview

A: First of all, consider the formula to find the linear approximation at any point a for function any…

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A: Linear measurement is one-dimensional. A linear differential equation is an equation where the…

Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

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Q: Q2- Find for the following functions :- dx 1- y = (Inx)/tnx 2- y = x cos-1 x - v1-x² +sin-1x

A: We have to find dydx for the following functions... 1. y=lnx1lnx2. y=xcos-1x-1-x2+sin-1x

Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

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Q: Find the differential of the function. y = 6 sin(60) dy

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Q: The linear approximation at x = 0 to sin(7x) is A + Bx where A is: and where B is:

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Q: Let y = tan(3x + 8). Find the differential dy when x = 3 and dæ = 0.1 Find the differential dy when…

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Q: Q2: find dw/dt at given value point for the following function x= cos°(1), y = sin²(1).= =-. 1 at t…

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