Suppose that f: R→R is a differentiable function, satisfying f(3)=5 and f(x) dx=8. 3 /x-s'(x) dx? What is the value of Your answer should be an integer.

Q: Find the differential dy of the given function. y = V3- x² dy

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

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Q: The equation of tangent line of the function 21 x3 f(x) = e7e dt %3D 21 x at x=1 is V21 e3087 (x-1)…

A: Given function is  f(x)=∫21x21x3e7t2dt Since at x=1, upper limit of the integral is equal to lower…

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Q: 1. If z = 2xy – 3x²y and x is increasing at 2 cm/sec determine at what rate y must be changing in…

A: Z is neither increasing nor decreasing at the given instant. A function is said to be neither…

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Q: Is the derivative of Jx* sin (1/x), x 0 h(x) 1o. x = 0 continuous at x = 0? How about the derivative…

A: Answer(a):

Q: Let y = f(x), where f(x) = 5x² + 5. Find the differential of the function. dy = X

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = In (√9-x²) dy =

A: Given: y=ln9-x2 To find the differential dy

Q: Find the local linear approximation of cos x at xo = cos 61°. T/3 and use it to approximate

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Q: Let y = f(x), where f(x) = 7x³ + 3x. Find the differential of the function. dy = X

A: The differential of y is the derivative of the function times the differential of x,

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = x/9 – x²

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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: Find the differential of the function y = f(x) . f(x) = (5x² + 7)/3 dy =

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Q: The linear approximation at x 0 to f(x) = sin(6x) is:

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Q: fy = f(r), how do we define the differential dy

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Q: Explain why the linear approximation to ƒ(x) = cos x at x = 0 is L(x) = 1.

A: The linear approximation, or tangent line approximation, of f at x=a is defined as Lx=fa+f'ax-a This…

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: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

A: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Let y = f(x), where f(x) = 3x+6/x+6 Find the differential of the function. dy =?

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Q: Find the differential dz of the function f(x, y) = 4y² + x²y-2xy and use it to approximate Az at…

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Q: Compute the differential dz of the function. z = x'y8 dz

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Q: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: Find the differential dy of the given function. dy sec x x² +9

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Q: What is the derivative of this integral?

A: We know that

Q: Let y = f(x), where f(x) = x4 − 5x. Find the differential of the function.

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Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 1 5x − 7 dy = | y = X

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Q: Find the differential dy of the given function.    y = x tan x

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Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: Find the derivative of y with respect to t at t=2 if a) y = cos (x) – cos(1+x²) and x = [sin(t – 2)…

A: The derivative of y with respect to t is:

Q: Find the differential dy of the given function. (Use "dx" for dx.) 8 y = 2√x + 4 dx *- (√x +++1)x dy…

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Q: Find the derivative of the function. r(x) = In| 4x + e* | Oa. 4+4e4* 4x +e*x O b. none of these…

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Q: Find the differential of the function f(x) = (x+4)^(1/2) dy =

A: Find the differential of the functionf(x) = (x+4)^(1/2)

Q: Let y=tan(4x+5). Find the differential dy when x=4 and dx=0.2

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Q: The derivative of y =e' ,In(sin 2x) is a) y = eln(sin 2x) sin 2.x b) y = e a(sin 2x), cos 2.r c) y'…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 1 4x - 7 dy

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Q: Find the differential dy of the given function. Xx + 5 y = 2х — 9

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Q: Find the total differential df to the function f(x, y) = x²y – xy? when x decreases from -2 to -2.01…

A: We will find out the required value.

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Given data is : dxdt=5et-3 , x0=4 To find the antiderivative

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

A: Consider the equation 5xy-5x3=15 Here, the objective is to find dydt in terms of x,y, and dxdt

Q: Find the differential dy of the given function. y = x(1 − cos x)

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Q: 7. Given y = sinh(e* +tan (2x)-cos (x+1). Consider | dy (i) et 1 dx 1+e2x 1+4x 1-(x+1) dy (ii) ex 1…

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

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: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: Find the general antiderivative of the function f(x) = +3 sin x - : 1 1+x?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.