3. f(t) = e-2t cos3t + 5e-2t sin3t ;Use property of shifting

Q: 8. (t² + 3) cos(5t) dt

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Q: Approximate (a) cos 0.8 and (b) cos 1/2 using the linear approximation technique

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Q: O. p. S sin 2x cos 3x dx 3dx /1 + 9x²

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Q: Q3 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: The given function is, y3secx2+y2=cos2x

Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: + b¬ + cx = 0 dt lution given by: - (A sin ßx + B cos ß.

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Q: (c) Show that the function z -- eX sin yt ey cos

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Q: y = (sin x +cos x) sec x = sec² x

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Q: If y = (3x)sin (2æ) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: 3. Explain graphically: cos x dx = 0.

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Q: e- + cos (xy) = (4 – 3z) (2 + 2.x), UIM 4. find ду ÚTM az cos (ху) — (4 — 32) (2- 8 UTM UT UTM

A: Partially Differentiate with respect to y

Q: If y = cos 3X find dy/dx: y = cos?3x = (cos 3x?. (cos 3x )?. %3D

A: Given, y=cos23x=cos3x2

Q: Find d-/dx² at the given point without eliminating the parameter. x=0+ cos0 and y=1+sin0 ; 0 =a/6,

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Q: Q3) find the soluation of differention equation 2) y' sin 2x = y cos 2x

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Q: T c •sinx, S* San* (1 + cosx)dydx 0, 0.

A: Given: The integration ∫0π∫0sinx1+cosxdydx To determine: The value of given integral.

Q: 1 Cos(2x)dx 0. (i) Using composite Trapezoidal rule with n = 2, 4

A: As per the policy of bartleby the provisions is to solve only one question at a time So I am solving…

Q: dz 1) Find ifz = 3 cos x – sin(xy),x =y = 3t - dt

A: NOTE*** As per bartleby guideline for more than one question asked only first is to be answered…

Q: Take the derivative of this integral.

A: Given

Q: Q3 Find dy/dx on the graph y3 sec /x2 + y2 = cos2x at point (1, 2).

A: We have to find the derivative  of given expression at point (1, 2)

Q: 17. Determine the value of fx dy - y dx, where x(t) = (cos 31, sin 3r), 0 ≤ ≤n.

A: The given integral is: ∫X x dy - y dx, where Xt=cos 3t, sin 3t, 0≤t≤π The components of the…

Q: (1 + cos 7t) 2 sin 7t dt

A: Here we use u-subsitution to evaluate the integral. d(cosx)dx= -sinx

Q: - ual2) V17 – cos(27at) (2 – 4t) sin(#) Given f(r) = edt, find the equation of the line tangent to…

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Q: What is the first step in eliminating the parameter t from the equationsx= 3 1 sin t and y = cos t -…

A: Given equations are x=3+sint,y=cost-2. To eliminate t from given equations, substitute values for t.

Q: 3. f(t) = 2e3t sin 2t 3est cos 2t %3D -

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Q: 3x d. Evaluate dx COS cos (3t – 1) dt

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Q: i. Jsin xcos 2x - sin 2x cos xdx

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Q: T For y 10 cos ( 10x 4 - its amplitude is its period is its phase shift is

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Q: cos-(siny) dx dy = -29

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Q: dz Find x? sin(2y – 5z) =1+y cos(6zx) -

A: This is partial derivative so differentiate it as normal differentiation of z with respect to y…

Q: ution of y" + 4y = cos 2x b

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Q: What is if z = x'y+ sin(xy²)?

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Q: のSX 3 +23 +5y +5y = e + 40 Cos loX-190 Sin lox

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Q: Determine an equation for the sinusoidal function shown. 2. 12 21 Oy = 0.5 cos[0.5(x+ x)] + 1.5 Oy,…

A: The general equation of a sin function is given by; y=A cos(Bx+C)+D Where; A→Amplitude of the…

Q: 7T, 0 cos( {*) cos(2y)dx 2gin( gx) sin (2) dy 77

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Q: Find the solution of the equation z az cos y which tends to zero as x o and has the value cos y when…

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Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

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Q: 2. If xy+Y find the value of dy dx2 5- at the point Co,-1)

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Q: b f sin'x. cos²x.dx ef cos(Inx).dx C-

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Q: Obtain the der a) cos(xy)=2y, find y'

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Q: d?s sin 3t + cos 3t dt2

A: Explanation of the answer is as follows

Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

Q: "+25y 4r sin(51) – 2e" cos(5t)

A:

Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

Q: 3.) Solve the equation using discontinuous function: y" + 9y = cos(2t) – U37(t)cos(2t) , y(0) = 0,…

A: We will find out the required solution.

Q: Find the value of zr» at the point (0, 3, 2) where a²y² + 2² – cos(ryz) = 10.

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Q: (2xsinx +3 cos y)dx-3x sin ydy 03 ....

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Q: (b) Determine cos(x²) 2x dx by using substitution method.

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Q: cos (2t) 23. sin' (2t) dt 3

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Q: 5. S sin(3x)dx (a) 3cos(3x)+ C (b) †cos(3x)+ C (c) – 3cos(3x)+ C

A: