H.wl: Find L St. sin 2t.dt -3t {e p1 p2

Q: Given æ = 11t – 10 and y = 121 sin t dy (i) dx dy (ii) dx? ||

A:

Q: dy Given y = In(tan 0), find 0 such that 4, where 0< 0 <T 2

A:

Q: H.wl: Find L{e-3t St. sin 2t.dt p1 p2

A:

Q: Given a6x CosT+Sy - .3x. -Siny+ 10x-e -*, defermine (1) T'=S(T) ax T'-

A: Given:T"=6x2y3-cosx+5y2-siny+10x2-e-3xTo determine:i  T'=∫T"dxii  T'=∫T"dy

Q: If y(t) = ∫0t x2sin3(x)dx = f(t)*g(t), then g(t) = ? a) 1 b) t^2 c) sin3t d) t2sin3t e) 0

A: According to question given that∫0tx2sin3(x)dx=f(t)*g(t)

Q: Given z = 64 sint+ 5 and y = 64 cos t + 4 da (i) dt dy (ii) dt dy (iii) dx || ||

A: Using derivatives of parametric function.

Q: Given e = 98 sint + 24 and y = 98 cost +3 da (*) dt dy (é) dt dy (é) da ||

A:

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

A:

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

A:

Q: Solve the following second order ODE dy dy + 2x dx? = 0 || dx with the initial conditions y(0) = 2…

A: The given 2nd order ODE is d2ydx2+2xdydx2=0, with initial conditions y0=2 and y'0=-1. The main…

Q: a - Find h (Stet sinh t sint dt)

A: The objective is to find ∫te-3tsintsinhtdt It is known that, sint=et-e-t2isinht=eit-e-it2…

Q: E valuate the Following in tegrals: sec (2+) dt tan (2t) 9.

A: Given that  The integral is  To evaluate the integral

Q: How many of the following questions have the same answer? dy =? I. y = cos(2t), x = sint = dx II.…

A: Since you have posted a question with multiple sub-parts, we will solve the first two subparts for…

Q: calculate dy/dx at the point indicated. c(t) = (et − 1, sin t), t = 20

A:

Q: Solve te following DE using laplace trancform - 3X ty =e cos2x when ylo) = 0 %1

A:

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

A: Let's do derivative of given function.

Q: Given z 13t 9 and y- 169 sin : dy dx d²y da?

A:

Q: X = Sint ond y = et If the while t = 0. AIO Bl -I c) -3

A:

Q: Given z = 8t – 18 and y= 64 sin t dy (i) da dy (ii) dx?

A:

Q: If z = sin(rry). and * = t+ s, y = t2² + 8 8z when t=0, s=1. at Find

A:

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  &amp;  y=3sin2t   So, a)…

Q: Q2- : Classify and Solve; d?y + 9: dt dy cos? t + cosht + sinh t + sin? t +3 sin t - 3t %3D dt?

A:

Q: b) Find fo dy for y = Vt-1 t = sec?x sint

A:

Q: dy Solve the equation sin (r) with initial condition y(0) = –1 using Separation of Variables. %3D da

A: Consider the equation: dydx=sin2xy,    y0=-1 To solve the given equation,…

Q: f(t) = cos(2t + 3) + e¬tu(t – 4) + tcosh²2t

A:

Q: Find dw/ dt at the given value for the following functio 1) w=x² + y°, x = cos(1), y = sin(t), at †…

A: The given functions are w=x2+y2, x= cost  and  y=sint and t=π. Evaluate w in terms of t as follows.…

Q: dT 4 dp = 0; T=To when p= Po dp pdT

A:

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

A: Find dw/dr using chain rule.

Q: find dy/dt y=cos^2(cot^7t)

A:

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

A:

Q: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

A:

Q: Q5.a) Find if sec?y = x? + t² dt Jsiny dx dy pcotx b) Find if tan²y = x² + VE² +1 dt dx

A: Solution:a) Given :sec2y=x2+∫sinxcosyt2 dt

Q: Given x = 70 sint + 13 and y = 70 cos t+ 22 dx (i) dt %3D dy (ii) dt dy (iii) -

A:

Q: the Yp Vvnich OllOWing is a particu y" + 2y' + 5y = sin t where A; are constants determined by…

A:

Q: D. Find dy/dx of the following and simplify x v4-x y= Arccos

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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

A:

Q: dy Find dt y = tan? ( sin 't) dy dt

A: Topic :- Derivative

Q: If y = (sin¬1 x)², show that dy (1 – x²) da? dy = 2. dr

A: y=(sin-1x)2 we have to show  (1-x2)d2ydx2-xdydx=2

Q: s zy dydz こミ0

A:

Q: h.w:2 Sit.e-3t sin 2t.dt f(t)

A: Answer

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

A:

Q: Given x = 12t – 48 and y= 144 sin t %3D dy dx dy dx?

A: We know dydx=dydtdxdt d2ydx2=ddxdydx=ddtdydxdxdt

Q: f(t) = (C + 1)te Bt sin At

A:

Q: Solve the following IVP: dy sin(z*)e %3D dx y(2) = V5 %3D

A: Use separation of variables method on dydx=sinx2ex3 dy=sinx2ex3dx Now integrate both sides without…

Q: Differentiate f(t) = (e + sin(2 – t))* %3D 29.

A: derivative of xn  = nxn-1 derivative of sinx = cosx derivative of ex= ex Derivative according to…

Q: Given a = 2 cost + 20 and y = 5 sin?t de (6) dt dy (é) dy (é) de ||

A: We have to find the derivative of given functions

Q: the given velocity v(t) = e2ti– sin tk and r(0) = (1,2,0) to find the position at time t = 1.

A:

Q: π ,t<. 3 b) Let y(t)= 1? + sint , find L(y(t)) 3

A: