If dt = y cos t and y = 3 when t = 0, then y = 2. A. esint + 3 B. 3esint C. sin t + 3 D. sint + 3e

Q: c) dx E (sin cos) dt

A: We find ddx ∫xπ/2   sint2   cost3 dt

Q: 7 sin°(e) cos"(t) dt

A: To evaluate the given definite integral

Q: Find dy/dx for the following functions i)x=3 cos t-2cos3t ii)y=3 sin t -2 sin3t

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Q: Find the value of dy/dx at the point defined by the given value of t. x 5 sin t, y = 5 cos t, t= O…

A: Given, x =5sint  y =5cost We have to find the value of d2ydx2 at t = 3π4

Q: You tart muesting at t=0 y co) =0

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Q: dy 2. If = y cos t and y = 3 when t = 0, then y = dt A. esint + 3 В. Зesint C. sin t + 3 D. sin t +…

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Q: The change in heat radiated by a body, detected by a pyrometer (non-contact temperature sensor), is…

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Q: Given: x = 0 – sin 0; y = 1– cos 0 d'y Find: dx?

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Q: Given z = 2 cos t + 35 and y= 9 sin? t da (i) dt dy (ii)- dt dy (iii) dx

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Q: Find dy/dx for the following functions i)x=3 cos t-2cos3t ii)y=3 sin t-2 sin3t

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Q: ddw? dt (C): If w = tan x and x = 4t³ + t ; Find

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Q: Given x = 2 cos t + 36 and y = 8 sin?t dx (i) dt dy (ii) dt dy (iii) dx

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Q: Given x 2 cos t + 2 and y 4 sin? t dx dt dy dt dy dx ||

A: First we will differentiate the given equation with respect to t

Q: dy d'y dx ' dx? 2. If y = sin 2x – 2 cos 3x,the find, at x 0

A: The given function isy=sin2x-2cos3xto finddydx, d2ydx2    at x=0

Q: Given the following DE (cos 2y – 3x?y?)dx + (cos 2y – 2x sin 2y – 2xy)dy = 0 -

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Q: Given x2 + 11x + 30 dx 1 + cos?(x) At what value of t does the local max of f(t) occur? f(t) :

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Q: Given a = 40 sint + 12 and y = 40 cos t + 29 da (i) dt dy (ii) dt %3D dy (iii) dx ||

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Q: Consider y@) + y" = 1+ cos( - t) Then a suit- able form of the particular solution can be written as…

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Q: dy If x = a (0 – sin 0), y= a (1– cos 0), then find dx |

A: Introduction :

Q: The integral cos(x – 3) dx is transformed into , g(t)dt by applying an appropriate change of…

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Q: a. The velocity of a car in meters per seconds travelled from its origin is given by v(t) = In (t2 +…

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Q: Given x = 2 cos t + 24 and y = 2 sin t dx (i) dt dy (ii) dt %3| dy (ii) dx || ||

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Q: d²y Answer: 1 . If x = t + cos t, y = sin t, find dx2 dx2 (1-sin t)

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Q: Given a = 2 cos t + 3 and y = 3 sin? t dx dt dy %3D dt dy da

A: From the given problem:   x=2cost+3  &  y=3sin2t   So, a)…

Q: dy 2 5. Find if y = sin (27t)+tan-(2Tt) dt

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Q: If x = t +cos t, y= sin t, find d^2/dx^2

A: Given that      x=t+cost , y=sint  Here we have to find d2y/dx2 .

Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

A: Given: At=et000cos tsin t0-sin tcos t To Find: To show that At-1 exists and then to find it.

Q: If x = 3 sin t and y =2 cos* t , then find dy at t = dx 4 O a. -0.67 O b. 0.76 O C. 0.56 O d. -0.86

A: Given x=3sin4t   ,y=2cos4t

Q: find dy/dx and dy/dx2, if : x = a(cosθ + θsinθ) and  y = a(sinθ - θcosθ)

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Q: Given x = 2 cos t + 1 and y = 8 sin? t %3D dx dt dy dt ||

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Q: d. t sin 2 dt COS dx 3

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Q: d²y +9 = cos?t+ sin? t + cosh t + sinh t +3 sint -3t dt %3D dt2

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Q: The velocity of a particle moving along the x-axis is given by: v(t) = 1 cos(nt), t>0

A: Use the defination of velocity than solve the differential equation by separation of variables.

Q: Given x = 98 sin t + 36 and y = 98 cos t + 17 da (i) dt dy (ii) dt dy (iii) da

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Q: A ) Find ſ cos 5t dt B) If y = x² + , x = 2t -5 then find dt

A: A)-     I=∫Cos5t dtlet 5t=uderivating both sides5 dt = duSo,I=15∫Cos u du = 15 Sin u +C…

Q: Given r 2 cos t+3 and y = 2 sin? t dr dt dy dt dy dr 13D

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Q: For which values of t is the curve concave upward? x=cos(2t) y=cos(t)

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Q: Given x = 2 cos t + 48 and y = 8 sin? t dx dt dy dt dy dx || || ||

A: We use parametric differentiation

Q: et cos(e') dt = (b) +C 3+4 sin(et) 3/4 sin-1 (c) (승교) dx = 16x?

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Q: Given a = 2 cos t + 26 and y = 5 sin? t dz dt dy dt ||

A: Simply take the derivative using basic concept of derivative.

Q: If u = x3 + y3 where x = a cos t, y = b sin t, then du dt

A: Solution

Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: Find the value of dw / ds at s = 0 if w = sin (e√r) and r = 3sin (s + π/6).

A: w=siner,  r=3sins+π6 Differentiating w=siner with respect to r, we get…

Q: e* cos e* dx J 4 + sin²e* A 1 tan-1 2 sin e* + C sin? e* + C 2 2 tan-1 B sin e* tan- 2 1 tan-1 2…

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Q: (dr Ifr=a cos ti +a sin tį+ at tan 0 k, find dt dr at t = 0. dr?

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Q: x=24 sin t + 6 and y=24 cos t+39 Find: 1)dx/dt 2)dy/dt 3)dy/dx

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Q: dy If x = 3 sin t and y = 2 cos"t, then find at /= dx Oa0.76 Ob.0.86 OC 0.67 Od.0.56

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Q: Given z = 74 sin t + 15 and y = 74 cos t + 17 dx (i) dt dy (ii) dt dy (iii) dr

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Q: Given x = 2 cos t + 24 and y = 6 sin? t dx dt dy dt dy dx || || ||

A: Let x = 2 cos t + 24 and y = 6sin2(t) Differentiate x with respect to t…

Q: Given x = 2 cos t + 18 and y = 3 sin? t dx dt dy dt dy dx

A: To find the following