Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = cos2(t),    y = cos(t),    0 ≤ t ≤ 6π   (b) What is the length of the curve?

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

A: topic - derivative of a function

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

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Q: Assume that x and y are both differentiable functions oft and are related by the equation y = cos…

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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

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Q: Given a particle is moving in a curve r(t) = cos  6t i + sin 6t j +  10t k. Find the tangential…

A: I have appended the formula used in the solution part

Q: The velocity of a particle moving back and forth on a line isy = ds/dt = 6 sin 2t m/sec for all t.…

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Q: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =

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A: Topic- Application of derivatives

Q: Let y = tan(4x + 6). %3D Find the differential dy when x = 5 and dx: 0.4 %3D Find the differential…

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Q: The velocity of a particle moving back and forth on a line is v = ds/dt = 6 sin(2t) m/sec for all t.…

A: Given:

Q: A particle moves on a straight line with velocity function  v(t) = sin(ωt) cos2(ωt).  Find its…

A: The given velocity function is,

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A: Given that,, Here, differentiate w.r.t. ,we get, We know that, To find: equation of the line…

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

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Q: A particle moves along the x-axis with velocity given by v(t) = 5 sin (t) for time t> 0. If the…

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Q: Find the equation of the tangent to the curve at t = 0

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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: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

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

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Q: Let y tan(4x + 3). Find the differential dy when z = 3 and dx = 0.1 Find the differential dy when r…

A: y=tan4x+3

Q: В. Find dz/əx , əz/əy at the point (1,1,1) if x³ + z² + ye*z + xz cos y = 0 .

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

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

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Q: (3) Let 4 = x²y² + x sin y, find 2 dy in terms of x and y; dx (4) Find the equation of the tangent…

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

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Q: Let y = tan(5x + 5). Find the differential dy when a = 2 and dx 0.3 Find the differential dy when x…

A: Given, y= tan(5x+5) Therefore, dy/dx = sec²(5x+5) .d(5x+5)/dx dy/dx = sec²(5x+5)*5 dy= 5sec²(5x+5)dx

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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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Q: with x=sec t and y=e". Then the value of dz evaluated at dt If z=tan In t= 0 is equal to (Correct to…

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Q: The velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for all t.…

A: given the velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for…

Q: Find dz/ðx , dz/ðy at the point (1,1,1) if x³ + z² + ye + xz cos y = 0

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