= e. In(16y), then fzz i 30 e5z In(16y) 25 e5z In(16y) 80 esz In(16y) 25 e In(16y)

Q: y= e fonksiyonunun d'y dy 11 + 27y = 27e dr 11z dr?

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Q: dz/dy for z = e^xy

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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: fm üli f (x,y,z)=x'+x*y *z ' + yz ?

A:

Q: If g(x) = ªſ*'[e'− In(2t+1)]dt, find g ''(x) . - dx -2 4 A + (2x + 1)2 Be-In(2x+1) 2 C (2x + 1)² 4 D…

A: Given that,      gx=ddx∫-2xet-ln2t+1dt

Q: Let z=xln(x2+y²-e*)-154xy, x=te, y=est. If the value of Oz when s=2 and t=1 is equal to Ae?+Be, then…

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

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Q: Evaluate dz where ci) .C is 1z+ Yzl =2 Ci) c is 1ztil=1

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Q: Evaluate fl. 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

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Q: Evaluate the followingintegrals.∫(z+1)√(3z+2)dz

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Q: Q2: Prove that: d csc-(InVx) dx -

A: The main objective is to prove ddxcsc-1lnx=-12xlnxlnx2-1. It is known that ddxcsc-1x=-1xx2-1.

Q: et f(r, y) (-(4r + y)) Then %3D ardy

A: The given differential equation is: f(x,y)=-(4x+y)7

Q: dy Find Z for y = (8+ x³ In x)ª + e3x

A: We have to find out derivative

Q: SSS 12z dV E where E is enclosed by z = x? + y² and z = 1 О Зл O 27 O 4T O JT

A:

Q: 3) Find dz dy for z = e

A: Solution: As per given date   z=exy  For finding dz/dy , we assume that 'x' is a constant.

Q: If g (x): A d dx [e' — In(2t+1)]dt, find g''(x) - -2 4 (2x + 1)² 4 B (2x+1)² Ⓒe*-In(2x+1) 2 D (2x +…

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Q: 39. f(a + 1+2 tag z + tag' x) dx = S (sec" z + 2 tag 2) dz tag z)' dz %3D tag z + 2 In Isec z| + C

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Q: Evaluate /f/2e(*+у*+ dV over B where B - {(a, у, 2) : а? + у? +2? < 1}. Тake п %3 3. SSS 2e(z²+y° О…

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Q: If z 6.57 (rounded to 2 decimal places) and y = 6.017 (rounded to %3D (a) the upper bound of x + y…

A: x= 6.57(rounded to two decimal places)  and y=6.017(rounded to 3 decimal places)

Q: The 300-lb block shown in the figure is kept from sliding down the inclined plane by friction and a…

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Q: Sf(x)dと SgCx)dx, suppeat 9 Explain why SfC dx 7 goa) Counter ekample to やU8e a your claim .

A: Use substitute rule unless the integral can be simplified and directly evaluated. Counter example is…

Q: If z = x2 – xy + 4y2 and (x, y) changes from (1, –1) to (0.96, –0.95), compare the values of Az and…

A: We have to use differential to find results.

Q: If z = x2 - xy + 8y2 and (x, y) changes from (1, –1) to (1.03, –0.95), compare the values of Az and…

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Q: *Pivd the general Seltion to the

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Q: * Evaluate SSS 12z dV E where E is enclosed z = x² + y? and z = 1 %3D Зл о 2л о 4л о IT O

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Q: Suppose that a) [15x²y; 0<x<y<1 f(x, y) = { 0; otherwise. Compute E(Xy), Var(X) and Var(Y). b)…

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Q: S(2y + 3)?/ y+ 2 dy

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Q: Let z=xln(x2+y2-e4)-3xy, x=tes, y=est. If the value of 2 when s=2 and t=1 is equal to Ae2+Be4, then…

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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: (z In z + 5)dz

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Q: Evaluate SSS 12z dV E where E is enclosed by z = x? + y? and z = 1

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Q: dy If y e+14 then- dz 70e+14 O6e+14 D 4ez+14 O 14ez+14 5ez+14

A: Given, y = e5x+14  We have to find dydx

Q: dy x fanx

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Q: b.Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x,…

A: Given that, v=yxy=vx

Q: D 45° F E Given FD = 6 in. FE = in. DE = in.

A: we have to find the unknown side length from the given figure

Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…

Q: Find f f'Lx) = ZR? +aX-S and %3D to FlO)=4.

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

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Q: In csch 4y d 3) tanh 4y

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Q: Evaluate SSS9e=+y²+=?)** dV over B where B = {(x, y, 2) : a? + y? + z? < 1}. Take = 3.

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Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

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Q: dy -2y 3cos3t – 11sin3t dt? dt

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Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…

Q: e obtained by r

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Q: Find h t Trans form of decivative for d²f and d' f dt3

A: