T 20) 12/13 90 3X 53 Sy-5 2X J00 108 1. y = y = Sign 00 H. of

Q: ind F(t)dt (don't include the +C) + C

A:

Q: EX Show that J (x) =2 sin X zm + Sali-J Cx)= L m + X4 /2 L2)(1)(E 2 (2!) Y2) 4 112 2.

A:

Q: Q2. Show that dx ax + by di dy = cx + dy di can be written as + yx = 0

A: The given system of differential equation is. dxdt=ax+by                     ......1dydt=cx+dy…

Q: dy when t = 7. dx Evaluate y = 2z? – 3z + 5 x = 4t +t t = z? +z+1

A:

Q: dt || y whent = 0, y =

A: Please refer to the image below

Q: Evaluate J S S dydx. r4x Jx2

A: To solve this question first integrating with respect to y and plug in the limit then integrate with…

Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

A:

Q: If x2 + y? = 169 and dy/dt = 5, find dx/dt when y = 12. (Enter your answers as a comma-separated…

A:

Q: 12. Use the substitution x = sec 0, where 0 < 0 < T/2 or T < 0 < 3#/2, to evaluate Vx2 1 dx x*

A: We will evaluate the given integral by using substitution method as shown below

Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

A:

Q: dy dæ 2 and dt at x = 3 if y = 3x? 4. Find dt

A:

Q: ) y = 3logst ) y deriv = (sech t) (1 - In(sech t

A: A function's derivative is the function whose value at x is f′. (x). The graph of a function's…

Q: find dy/dt. y = (t-3/4 sin t)4/3

A:

Q: QS A) Find IF y = - Ve IF y =-Vt and t sinx

A:

Q: Q3.a) Find if y + SE 1 dt = xy (secx dx sint+1

A: My dear, as per our guidelines we can help you in solving only first problem. Rest of them , you…

Q: 7 dt, where x> 2 Find dx for y = J 31+7 3

A: We shall use the Newton Leibniz formula

Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

Q: dy dt 1. y=V(3t2 - 2t + 1)(t2 – 1), 12/07/2021 18: 54

A: Given that       y = √(3t2-2t+1)(t2-1)  Here we have to find dy/dt .

Q: Use the substitution formula to evaluate the integral. T/16 (1 + etan 4x) sec 2 4x dx 4e

A: Given that ∫0π161+etan4x sec24x dx ...........................(i) Substitute u= 4x  dudx=4 ⇒dx=du4…

Q: dy when t = 7. dx 13. Evaluate y = 2z? – 3z + 5 x = 4t' +t t = z? + z+1

A: Derivative of the function decides whether the function is increasing or decreasing. If the first…

Q: -2 Evaluate the integral: ² ft² n s teu du ds dt

A:

Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

A: A line integral is the integral of a function along a curve. The function can be scalar-valued or…

Q: (i) J. dt 6. –t²

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Q 2. Determine dt (i) J." -t2 4 (ii) ſe-t sin tdt. 4 (iii) J 73_2x² – 7x–4 -2х? —7х-4

A:

Q: Evaluate the integrals

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

Q: Suppose 4x? + 9y² = 36, where x and y are functions of t. If = 1/3, find dx/dt when x = 2 and dt y =…

A:

Q: d tant lea) de tan' L) Itx? 2x THlege THe" ux 2) la 2x ln x Ids 2 lox t 2 y de 4(2/ax+2) 3) fL7)-6…

A:

Q: t²e*dt dz J2r

A: on solving this we get the

Q: dz Find dt(t=1,s=0) when z = 2x3 + 15y3, where x = t2 - s and y =t+ 2s2

A:

Q: Express in the form x + jy (3) sin(t/4+j2)

A: Complex Number Question

Q: Compute each derivative. (3r y7-32x y3+ 5xy) 5. e 1. ду a 3x abc 6. fa if f(a, b) = e° sin(a +b) 2.…

A:

Q: Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z =t², (0 <t< 1).

A: As per the question we are given a line integral, which we have to evaluate around the curve C.

Q: a) dt 9 =dx xVln x b)

A:

Q: Evaluate: L{t f -t e2t Cos t dt}.

A: Evaluate: Lt∫0te2t costtdt First of all we find    L(cost)=ss2+1L(e2tcost) =…

Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 6.  (Enter your answers as a…

A: We would differentiate the given expression implicitly w.r.t. t, ........................(1)

Q: Q2: Sdve the differential eqpeation d²y =20"t 9Sin 2x -2Cos 2x %3D

A:

Q: Find dy/dt. y = t°(t4 + 2)5 O t°(t+ + 2)+(29t³ + 18) O 9t°(t+ + 2)^(20t* + 2) O 180t4(t+ + 2)4 O…

A: We are going to solve

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

A: Answer

Q: dy Find dt y = 3t(21 – 5) $ II 히

A: The product rule of differentiation states that ddx[f(x)g(x)]=g(x)ddxf(x)+f(x)ddxg(x) The chain rule…

Q: Evaluate J.J. xy² dx dy 2 20 30 20 -30 -20 2/3 2/3

A: In the given question we have to choose the correct option from the given option . In the question…

Q: 26. (4D4 — 24D3 + 35D? + 6D — 9)у 3D 0. е"C, + с2x) + сз cosh }x + c4 sinh }x. ANS. y =

A:

Q: Assume that y= 5x and de/dt = 2. Find dy/dt. Select one: 10 O 5 O 2 1

A:

Q: find 04 O B O 7 O -12 af ду dy' given f (x, y) = e + 2xy² – 4y at (0, 3) -

A:

Q: dy(t)25dy(t) + dt + 2y(t) = %3D dt2

A:

Q: 1 dt xy secx Q1.a) Find if y+J sint+1

A:

Q: 2t + 1 What is the indefinite integral of dt t3 -8t + 21t – 18

A:

Q: S 6 ttan t dt = %3D dx Jx

A:

Q: 4 2 fof five y/2 Evaluate ex? dxdy by changing the order of integration.

A: Let I = ∫04∫y/22ex2 dxdy Given Region is equal to: y = 0, y = 4, x = y/2, x = 2

Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.