8tan4x dx. Q. S 3 None 8log|sec4x| + c 3 2log|sec4x| + c 3 2log|sec4x| + c 4

Q: Evaluate 11-x [[ x³y²¹ (1-x - y)²dy dx -10 9π/25 O 1 Non of the above O TU 9π/28

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Q: 2+i (a) Evaluate dz , along the line x=2y.

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Q: d'u = (1+3xyz+x*y°=²)e² dxdydz xyz If u = e-,show that 1+ 3xyz + x y:

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Q: dy If 2y = xlnx, then dx (In x)xinx (xinx) In x (b) (d)(In x)xanx) 2

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Q: Find y(0) and y(inf) for the following: a.) Y(s) = (0.9*(s+1))/(2.1s^2+5s+16) b.) Y(s) =…

A: Consider the calculation for the sub-part (a). Substitute s = 0 in Y(s) and simplify to calculate Y…

Q: N. R dy dx where M,N, P.Q and R are algebraic expresions.

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

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Q: For S dx, x = 1+ Vx O x = u^4 O x = u^(1/4) x = u None of the choices ООО О

A: We use those substitution which makes integral easy. Hence, x=u4 This is the required substitution.

Q: 3. (x²)(d²y/dx²)+x(dy/dx)+(2/y³)=0 (hint: set x=e')

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Q: 2 dy U=x-4 Eilsy =4-24 ذا كانت %3D

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Q: Find an expression for dy/dx. y= (u+5)(u-5) u= x2  + 7

A: Given expression are  y=u+5u-5=u2-52                                Using a+ba-b=a2-b2=u2-25…

Q: Ir 9- ((2, y) | 2553,1SyS 3): D then: dz dy = %3D

A: Given D={(x,y)|2<=x<=3,1<=y<=3}

Q: y z = x + show that : 0.

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Q: dx 7. JIVa² – 2x + 5 (hint: let æ² – 2x + 5 = (z – x)²) -

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

Q: 2. x"(t) – 4x'(t) + 4x(t) = 4e²t; x(0) = –1, x'(0) = -4 %3D

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Q: dy Find if y= e©o0s4z dz 4sin4x. ecos4z None -4sin4x. e³in4z -4sin4x. ecos4z

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: (b) Hạ: u < HO,n = 30, t = 2.431 = 0.011 P-value %3D

A: Given : Ha : u &lt; uo  n = 30  t = 2.431

Q: +x 5) Let z = f(x² – y²). Show that y ду əx az

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Q: (1)F (s)= s +9 2s2 +s -1 %3D

A: Given: L-1s+92s2+s-1

Q: 2 2 Va? +x + Va? -x² If y = Ja? +x? - Va .2 Show that dy 2a 1+ 2 a? dx 3 Va* – x*

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Q: Let A = {x E Z: 8lx} and let B={EZ:12lx}. Then None of these ВС А O ACB O A=B

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Q: [ u#(u – 1)"-1 đu (1+x!/n dx = n

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Q: If f(x,y,z) = In(xz) – 2xy2z, find fzxy at the point ( 0.5, 1,-1) a) 2 %3D d) – 2 e) - 4 g) None of…

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Q: Find an equatlon Of the ine Through G1,2); Perpendicular to me 2x+ 5yt 8=0 line

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Q: a) Find as when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y,x = 2t + s, %3D %3D y = 2s - t.

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Q: 10 Let y = ( 2x + Then -A(2x + 10)" (2- 10)°, dy = A[ 2x + 2 - where A = %3D C = %3D

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Q: For any 2 RVs X and Y {E(XY)}² < E(X?E(Y²)

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Q: 2y4+x+ хуз dy dx a. y = x b. y = x8 – x4 C. y = Vx8 – x4 d. y %3D х — 1 e. Not in the list.

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Q: 4. x t +5 and y = 5-t for 1<t = %3D t

A: We are asked to find the domain of the graph.

Q: 1.) y = ,"(x* + )d. 3 1.) у 3 /1-х2, 2.) у %3D S Vu du

A: Newton-Leibnitz rule :                ddt∫g(t)h(t)f(x)dx=f(h(t) dh(t)dt   + f(g(t) dg(t)dt Note…

Q: If f (x, y) = x² y² – xy³ then find ²f at (1,0). дудх O 1 O -1 O None

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Q: 3(1 + P) = 2ty(y³ – 1) dt %3D

A: Let us consider the differential equation dydt+P(x)y=Q(x)yn It is known as Bernoulli's equation…

Q: xy Let z . Then: 4x2 – 5y? | az dz ду

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Q: 7 Suppoe | f(x) dæ = 3, f(x) dx = 14, | f(æ) dæ = 7. %3D Then 8. f(x) dx Σ I F(x) dzæ = Σ

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Q: 2 sec 0 r drde = x² + y² dydx %3D 0. True False Reset Selection

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Q: If y = In(x² + y²) then the value of d at the point (1,0) is %3D Select one: O a. 0 O b. 1/2 O c.1 O…

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Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

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Q: I Findk the GS op the bE (x+3y)kk +(3x+g-) dy mo 50

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Q: 4. Which of the following is an exact DE? A. (x²+1)dx-xydy-0 B. xdy+ (3x-2y)dx = 0 C. 2xydx…

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Q: 11. f (x, y) = ery subject to a? + y? = 16 %3D

A: The objective is to find the lagrangian multipliers for fx,y=e2xy subject to gx,y=x2+y2-16. To solve…

Q: Í (x)dx, iff(x) = Vx -k +1;k-15x <k, k = 1, 2,.n.

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Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: S-ydx + xd - ydx + xdy, C: y² = 3x from (3,3) to (0,0) O 4 O O 2

A: Solution is given below:

Q: Find y for the following ey ex-e %3D Select one: 1+y O y= x +y O y = ex-y exy xexy+eY Oy= -yew xexy…

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Q: (2? + y? + 1) dæ – (æy+ y)dy= 0 - %3D x +1 (x + 1)? Option 1 Option 2 (x + 1)-3 (x + 1)-1 O Option 3…

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Q: 2x + 2. Find y' if e?* 3y = x² – In (xy³).

A: To find y' e2x+3y=x2-lnxy3

Q: 3. (36D² – 60D + 25)y = 0 5x a.y = Ge+ Ce 5x b.y = Ce+C,xe 5x c.y = C,xe + Cxe 5x d. none of the…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: dy a. Find of the following. dx 1. у%3D 4u? + би — 2 and u — 4x? + 8х + 1 - 2. у%3D uVu +1 and u %3D…

A: Here we have to find dy/dx.     Note : As per our company guidelines we are supposed to answer only…

Q: 3. Jo F(x)dx=-7, S9(xdx= -12, S 9cx) dx - -15 9(X) dx = -15 Find the value a Such that (af(x)…

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Q: Let X = n(µ,4) and Var(2x) = E(4–7x) find %3D H.

A: Given: a random variable X follows normal distribution. Mathematically, X~N(μ,4) The expected value…