-5 d (b) / (100 – |17|)dæ (c) dx In(w² – 1)dw) 5

Q: 7) S fysinx'dxdy 1 ans:- (cosl–1) 6 4 -y

A:

Q: Q22. If y=tan x+ tan dy is: -then dx 2 (d) 1+x (a) 0 (b) 1

A: Given function is                                          y=tan-1x+tan-11x we have to find…

Q: -1-y 3) Evaluate the integral dxdzdy?

A:

Q: dy In(3x + 7) Find for y = dæ 9e5z dy %3D dx

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Q: Show for Re(z) > 1 dx = r(2) ((2). et - 1

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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: If k> 0 such that O St the above 4* dx = 3 then k = 2ln 2

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Q: dy de Xoy. -Secxy)

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Q: If f(x) = exp(-x).In(x), then , when x=1, df/dx is 1/e C 2/e O e nonexistent O

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: die ktvaate et:rlrs erziv. 2l y=a* + &r-- 5+e" Kl) =

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Q: dy If y = e8z+13 then- dx O 7e8z+13 O 13e8z+13 O 9e8z+13 O 8e8z+13 O 104e8z+13

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Q: d Prove In Jax| dx In x for any constant a. dx

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Q: In 8 In y S S e*y dxdy x+y

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Q: 100 e of f (s) = %3D s (s+2)2(s+3)

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Q: d Prove that (x") = n x"-1 dx

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Q: - Evaluate the follwoing | r" exp(ax")dx where a + 0 and m+l = 1, 2, 3, ...

A: Given integral is, ∫xmeaxndx Substitute, u=am+1nxm+1dudx=m+1am+1nxm+1dx=1m+1am+1nxm+1du Then,…

Q: 25-x² dx In if we let u = V25 – x , then udu =-xdx.

A:

Q: 7. Show that Sx" Inx dx =Inx-+ c. n+1 %3D + C. n+1 n+1]

A: Using integration by parts we can prove the given integral.

Q: ex+y ди 21. If u = show that ax ди = u ду - ex+ey'

A: The given function is: u=ex+yex+ey

Q: 18. y = (In 0)" > dy de = T(In 0)-1) () T(In 6)(-1) %3D

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Q: O prove that : (2) DO 2x e dx a e +b where a, b >o

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Q: 25 - x2 In dx , if we let u=V 25 – x2 , then udu = - xdx. A True B False

A: On solving this we will get

Q: -2 -In x SLy e dz dx dy O 7/24 O 7/48 O 5/48 O 47/24

A: We have to find the integral.

Q: dy 3) Determine the of : In (ху?) %3D х у dx

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Q: dy 3. Find dæ if y = In (aVæ +1).

A: Given,            y=lnx3x+1

Q: 2) Show that La- (1 – x²)P',(x)P'm(x) dx : 21(1 + 1) Sim. 21 +1

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Q: Find the derivVative of the function. 5. y= In 8v +5 dy dv %3D

A: The objective is to find the derivative of the function.

Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

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Q: Find the G.S.of the DE. (ytu dy=D0

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Q: O Fined s where c is :-12-11=4 the ly Porbolic 7-2/4/2121

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Q: - 3+ In x 3+ In x dy show that dx 2. (i) Given that y = [2] x(3 + In x)? 12 (ii) Hence evaluate dx .…

A: (i) Given : y=-3+ln(x)3+lnx Therefore, taking derivative both sides w.r.t x :…

Q: (z In z + 5)dz

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Q: dy B] If y = e" In(u) and u = V1-x2, Find dx

A: To find

Q: (2823 у — 3D 252*у — 6 sin 3а) dx (20x°y3 – 21a*y?) dy 4.4 - -

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Q: Please see the attached problem. Thanks!

A: Given:

Q: dy y(ln y- In a+1) dx 1 C = -In 1 C = In O Option 2 Option 1 1 C =-In None of the choices O Option 4

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Q: If In(ax)dx = 4, then a ( In(ax)dx %3D 1 4

A: we have to find the value of a

Q: Find the exterma R-{ (ny ): xy zo} 2. F(xry) = x² +y?- メッ ×り

A: To find extrema first we differentiate the given function with respect to x and y, then after…

Q: x2 1 dr dy = a° In(1+ x² + y? 3

A:

Q: dw If w = x2y sinz - 3zey, find dz 6. O a. dw =x?y cosz - 3exy dz O b. dw =2x2y cosz- exy dz O c. dw…

A: Find the partial derivative of w  with respect to z

Q: 4. Use Green's Theorem to evaluate | ay dx + (1 – ry) dy where C is shown below y (14) F1,2), (1.1)…

A:

Q: dy (a) Find if y = (In x)=². dx

A: For (a), dydx=lnxx2'       =ex2lnlnx'        =ex2lnlnxx2lnlnx'        =ex2lnlnx2xlnlnx+xlnx…

Q: dy dx If y=e+19 then O 19e+19 O 4er+19 O 57er+19 O 3er+19 2er+19

A: Please see the answer in Step 2

Q: In(v¤) dædy 6. 15. Calculate ry

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Q: Let G) = Jtan"(x)dx Find 18G(1) + 140G'(1). %3D O A. 0 O B. 357 OC.No Answer is correct OD. 140%…

A: Given: G(t)=∫t2t3tan-1(x) dx

Q: 2s+2 ds = In|s| – In\s + 2| + C %3D s3 +3s2+2s

A: Here, we are solving only 1st question and for the remaining question post the question again.…

Q: Q/ Find an integating factor for the diff- equ. 2y dx + (3y-2x)dy20? to

A: Conversion of non exact differential equation  to Exact differential equation. Given differential…

Q: L{sin(JF)} = V %3D 4s 2.s2

A:

Q: Q6/ If Y= 5u3 where X=u2, u=vx. find dyldx. * dy_ dy dx_ 15u2 dx du' du dy ,dx 15u? du' du 15u 15x…

A: Topic- derivatives

Q: dy If y = e" In(u) and u = V1-x2, Find dx

A: y = eu ln(u)       and   u = 1-x2 dydx = ?