Differentiate y = cot(t) + cot(1/t).

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)

A: We have to eliminate the parameter and find the cartesian equation.

Q: Find y= sin (1) i %3D dx

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Q: sin t cos t dt Jo

A: since u have asked multiple questions in a single request so we will be answering only first…

Q: How to find the characteristi dx(t)/dt=Ax(t)+Bu(t)

A: Given: To find the characteristic equation of the system: dx(t)dt=A(x(t)) + B u(t)

Q: Find tan * using lutegration by parts

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Q: nasin(hx) cos(bx)dx

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Q: Find the total differential, given: (b) \theta = arctan (y/x)

A: Let us consider the function z=f(x,y)  The partials derivative are obtained as…

Q: | (sin t)V1+ cos t dt

A: Given function is ∫sin t 1 + cos t dt We can solve this by substitution.

Q: Find the points on (t + sin t, t − 2 sin t) where the tangent is vertical or horizontal

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Q: find y'' for the curve cosx-siny=4

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Q: 28. Se cost sin 2t dt

A: ∫0πecostsin2tdtSolution :∫0πecostsin2tdt2∫0πecostsintcostdtlet, cost=x-sintdx=dxsintdx=-dxat…

Q: 33. cos y? + x = e %3D

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Q: cos y` +y = tanck) %3D

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Q: Find integral.

A: The given integral ∫cosxsinx dx can be evaluated as, Put, cosx=t Taking differential on both sides,…

Q: cos(48°) Use differential to approximate the value of

A: Cos 48° The nearest value to 48 whose cosine value can be taken is 45.Let us consider :x = 45° and…

Q: 3 sin (t) cos“ (t)dt

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Q: EXAM Q1-If x= cot-1 VE, y =,-. find dy d2y dx' dx2 at t = 2.

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Q: sin(y)dx + cos(y)dy = 0 by exact

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Q: 6- y" + 4y = cot(t)

A: Given:        y''+4y=cott        4yt+d2dt2yt=cott The differential has the form        y''+py'+qy=s…

Q: 2x g(x) = |VI+t? dt 1+t2 dt %D

A: To find the derivative

Q: Find of xy = cot(xy) dx

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Q: QI Find dy for dx dt

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Q: Find ay Sin(x+y)=Cos X t cos y

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Q: 2. Find equation of the tangent line at the point P given by t = where x(t) = cos (t) %3D y(t) =…

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Q: Differentiate. y = e cos x + Cos( ex)

A: Given- y=ecosx+cosex To find- The value of the derivative of the above function. Formula used-…

Q: dy Use implicit differentiation to determine dx given the equation a · ev + cos(x) = y². dy

A: We will do implicit differentiation.

Q: QI/ Find dx 少 for Iny=ex).csch"()

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Q: sinx Find y= [ e dt COS X

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Q: sin(y) = -5x dy Also, dt 10. dx Find when y = -T. dt

A: Consider the following: Differentiating the function with respect to x on both sides, we have,

Q: Find dy/dx  if   x4= cot y

A: First diffrenciate with respect to x and y.. Then simplyfy.

Q: Find of xy = x + cot y dx

A: This Question need implicit differentiation

Q: dx = ( sin 2y – 2x cot y) dy is ? -

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Q: Differentiate y= cosh vx

A: Given, y = coshx  We have to differentiate it.

Q: find ds/dt. s = tan t - e-t

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Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

Q: L sin(t) dt

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Q: dt 1 . sec t

A: Given integral is ∫dt1−sect The expression 11−sect can be written as follows 11−sect=sect1−sect+1…

Q: (g) sin vt dt.

A: Intigrating the given equation.

Q: x +y-y° =5

A: The given equation is x2+y-y3=5 We have to find dydx=?

Q: EVaLuateAt W= X X=cos't Y=cost sin

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Q: cos(xt) cos (sin(at)) dt D. tan x dx =

A: The question is taken from the calculus in which we have to find the value of the given integral, We…

Q: g. cOS x Vsin x dx

A: Let sinx = t

Q: (sinx + cos y) dx dy

A: Given that The double integral  To evaluate the double integral

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: I am going to solve the given problem by finding the arc length of the given parametric curve to get…

Q: sint dt de + 0 cos t – tan t

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Q: Differentiate the fol y = (sin x)(lnx) a)

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Q: 13. J sec0 de 14. J cot4x csc4x dx.

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Q: t sin (=) dt du

A: