Let the velocity of a particle be given by v(t) = –sin(t). What is the displacement of the particle from t= 0 to t = 2T? What is the total distance traveled by the particle from t = 0 to t = 27?

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Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy Find the first…

A: Given that y is a function of x defined implicitly by the equation  siny=4x+xy

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A: To find: The integral of ∫cos2x·sin3xdx. Formula used: Trigonometric formula: 2cosA·sin…

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Q: 44. Use the accompanying figure to show that sin-x dx. sin x dx y = sin y = sin x

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A: Find the value of x

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A: Here we will find the antidarive.

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A: Here a function is given and we have to find the equation of the tangent line in the form y=mx+b at…

Q: Evaluate ∫ a cos x dx and ∫ a sin x dx, where a is a constant.

A: Given∫a cos x dx

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Q: At what points the curve x = 2a(cos(t))-a(cos(2t)), y = 2 a(sin(t))-a(sin(2t)) has vertical and…

A: Given: The curve equations are shown below. x=2acost-acos2ty=2asint-asin2t Calculation:…

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Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. tan2y dy = sin3x dx

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Q: The height (in centimeters) at time t (in seconds) of a small mass oscillating at the end of a…

A: We find the velocity function by differentiating h(t) with respect to t

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Q: I= ( cos(In(x)) dx 13- I =

A: GIven that: I=∫cos(ln(x))xdx

Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy Find the first…

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Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Recall that the linear approximation of a function y=f(x) at x=a is given by y=f(a)+f'(a)(x-a) Here…

Q: Without using a calculator, find the distance traveled by a particle with position (x, y) as t…

A: The distance travelled by the particle is the same as the arc length as varies within the interval…

Q: . The voltage V and the current i at a distance x from the sending end of the transmission line…

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A: This is a problem of linear approximation.

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Q: y = sin(Ax + B)

A: We will find the Differential equation as following.

Q: If y3 + y = 2 cos x, find the value of d2y/dx2 at the point (0, 1).

A: given, y3+y=2cos xwe have to findd2ydx2 at point (0,1)

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A: We have to evaluate given integral Concept:

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Q: find dy for ee Sin (メ+34) dx

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Q: dy find the dx +Ince 义 9 = sin In Cl+e)

A: The given problem is solved below in detail.

Q: sint In(cos t)dt

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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

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A: We take the help of integration by parts in solving this problem

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A: Follow the procedure given below.

Q: Consider the implicit function. ev = sin (2x) dy in terms of x. dx Determine the formula for dy dx

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Q: Find for the following function: dx 1- y = sin-1 V2x + 3

A: See the attachment

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Q: The approximation of I = , tanx dx

A: The solution is

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Q: Using a similar method to above, that is, integrating by parts twice, the following result may be…

A: In this question we have to prove Integration by using Integration by parts.

Q: Find the length of the curve y = ln (sin x), π/6 ≤ x ≤ π/2

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Q: COS T dx sin' a

A: given that a integration we solve by using integration method . Here i attached solution of this…