|| (6 y x 2 y )d A R=[1,4]x[0,3] 2 .A O .BO 2c0 9 .DO 9, 2/9

Q: Consider ,- (x3+y²). Evaluate dx² O (9x4+6x)e «³+y?) O (6r²+ 3x)e (x³+y?) O (6x4+9x)e (x³+y?) O…

A: The formulas used in the solution are as follows: 1. Chain rule: df(t)dx=dfdt·dtdx 2. Product rule:…

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e when r = 2, s = 1,t = 0.

A: We have to find solution

Q: If f(x, y) = xe2y + 6xy, then is dydx given by: e2y + 6 등 2e2y + 6 2 O None of these O 2xe2y + 6…

A:

Q: (トタりナーそJ0 on メou sqo とてラメテ0 'hらトラメe 1(h8)3-9 4 トtト×ピーメピ(トタ)さーそ ト×-メと -(ドメ)きーモ

A:

Q: f tan(z)dz C, = {z € C: -|= 5} CL

A:

Q: Q4/ if f(x.y)=x-y and g(x.y)=3y prove V2) gVf-fVg g? %3D

A:

Q: f (t) = 3e" cosh (In 2r -2t

A: Given,                 f(t)=3e-2tcoshln2t

Q: for: m -} answer fx) = x2-x at x=-1 anjwer for: 4-4, = m CX -X,) dy dx m= m- 2x-X m = 26)- (-1) m=…

A: Given:        f(x)=x2-x  at x=-1 This is in the form of y-y1=mx-x1    y-intercept form at x=-1 is…

Q: (a) (Xn+r)nzo for fixed r≥ 0,

A: Markov chain: A Markov process with discrete time and discrete state space is known as Markov chain.…

Q: Q2/ A/ Find the and ar * iff (x.y) = x - xy, x=r² +s and y =r-s as

A:

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: dy 1. If a? + e 2xy = r + (y-2), find when r 0. dr2

A: We have to find second derivative at x =0.

Q: Q3) If f(x, y") = x + y? + Vãy find: af(x²y) and Ty) ду afxy)

A:

Q: H In OJ, GH = 9, KL = 4x + 1. Find x. R 5. 5 S. GK

A: Given: GH=9,KL=4x+1  If from a centre a perpendicular is drawn to the chord, then a chord is divided…

Q: [38] Evaluate f, 40yds where S is the portion of y=3x2+3z2 that lies behind y=6.

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Q: Let A = {x E Z: 8x} and let B={rEZ:12lx}. Then * ACB ВСА None of these A=B

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Q: If f(x, y) = 7xey + 7y Inx, then is given by: дудх O 49e5y + 7/x 35eby + 7/x O 25e5y + 7/x O 35e5y +…

A:

Q: 9. If y = , find at x = 1. x3-: \2x5-1, А. — 28 В. —13 С. -52 D. 13

A: Consider the following equation: y=x3-22x5-14 Differentiate y with respect to x:…

Q: af Given f(x, y) = In(7x² + 9y²) then

A:

Q: aw b- if w = x + 2y + z2, x , y r2 + Ins and z = 2r , find the value of ar .rk)

A: We will solve the following

Q: A- If y = e3x and y = e-3x , prove that: - d²y dx2 – 9y = 0

A: The solution for the above question is as shown below.

Q: 4. (a) If y = A + Bx + Cx2 and yo, yı, y2 are the values of y corresponding to x = a, a + h, a + 2h…

A:

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

A:

Q: Find when r = 2 and s = 0, if: as z = xy² – x – y x = y = ers 1+s

A: Here given that z=xy2-x-y, x=r1+s,y=ers So, ∂z∂s=∂z∂x∂x∂s+∂z∂y∂y∂s        =y2-1-r(1+s)2+2xy-1ersr

Q: If RX = 18. XS 10, and RT = 35, then YT

A: It is given that RX=18, XS=10, and RT=35 In triangle RST, the line XY is given parallel to the base.…

Q: If x2 + y2 = 2st − 10 and 2xy = s2 − t2, find ∂x/∂s, ∂x/∂t, ∂y/∂s, ∂y/∂t at(x, y, s, t) = (4, 2, 5,…

A: If x2+ y2 = 2st − 10 and 2xy = s2 − t2,To  find∂x∂s,∂x∂t,∂y∂s,∂y∂t at (x, y, s, t) = (4, 2, 5, 3).

Q: Let X ~ NB(r, p). Show that E(X*) =-E(Y – 1)*-1 where Y ~ NB(r+1, p). а. b. Use this result to find…

A: It is given that:

Q: B = {(x,y xs2, -a sy s3, 0£21} SS, x*yz²dV 2 'B

A:

Q: S- - ydx + xdy, C: y² = 3x from (3,3) to (0,0) 01 0 3 O 0 2

A:

Q: b с a+х b+у с+z a [E] If A = |p qr = 6, evaluate det (A) where A = 3x Зу 3z -p -r

A: This question is based on determinant properties.

Q: -号。 - 4X u (x,o) =3 e 2 , ニ0 y2 Ansl ux,y) = 34(メ+) Ans.l ucx,y) 3 e %3D

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Q: Find x E R that satisfies -2 , – 02 + 2 vz U2 det = x det + – ö4 2 0 + 03 U3

A: The key concept to solve the given problem is that : The determinant of a matrix remains unchanged…

Q: b Sx³sin(2x)dx= [x²s(2x) dx = 27x²³ - 24 W 64 Given : Find bif s sbst

A:

Q: 1 If Y = x? dy = ? then dz · +c O 22? O 2x 2 dy If y = 6x + 2.5x² + 7x + 2 then dr

A: 1. Given y = x2 So dydx = ddx(x2) = 2x Answer: 2x

Q: If X-B(x; 10, 0.25), which of the following is P(2<Xs4), approximately? Lütfen birini seçin: a.…

A: From the provided information, Number of trials (n) = 10 Probability of success (p) = 0.25 The…

Q: 1 f f(x) = : R → R, Vx2 – 4 At how many different integer points x is discontinuous? 25 - O A) 3 O…

A: We have f(x) = 1x2-4Clearly f(x) assumes real values for all real values for all x except for the…

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

A:

Q: If x – y = 4 and xy = k what exp ression is equivalent to x² + y² ?

A: We have, x-y = 4                           ......1xy = k2                             .......2 To…

Q: df Let f(x,y,z)=xy+z?, x =s², y =2rs, z =r?. Find when S =1 and r=5. ds

A: Given that f(x,y,z)=xy+z^2 ,x=s^2 , y=2rs ,z=r^2 We have to find ∂f∂swhen s=1 and r=5

Q: is given by (X – Y) ± Z V where Z. is a real number such that PİZ > 7.) 4 for Z ~ N(0, ).

A:

Q: Q.1) Evaluate, (a) 3y In (y) dy 7+1 zp- (ь)

A: Find the integral

Q: Q5/ If w = f(x,y),x = rcos0,y = rsin0 show that: af af 5² + 1 dw Əw. -)² + ar r2 a0 дө

A: The chain rule can be used to calculate the derivative of the complex functions. The function which…

Q: -v-S vdu G) - S -r lee) dx 2 (보라2) 2 (x²t2) - x2 2 (R?+2) ㅜ 2 (x? qz) - (x? $2) z (? t2) In Ix? tz…

A:

Q: Vx Sn(l+x*) de 23/2

A: Using the substitution ... Explanation of the solution is given below...

Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf(2, –1, 1) = - A) * V3 B) 11 C) V3 D) E)

A: The given function is:    f(x,y,z)=ln2+x2-2y2-3z

Q: Evaluate the convolution between h(t)= e2u(t), and x(t)=2u(t).

A: From the above details we have,

Q: 17. f (1,y, z) = x subject to z? + y? + 2² – z = 1 %3D

A: Let h(x, y, z)=x2+y2+z2-z. We now have ∇f(x, y, z)=(1, 0, 0) and ∇h(x, y, z)=(2x, 2y, 2z-1). Let λ…

Q: Q3) If f(x, y?) = x² + y2 + Vxy find : af(x²,y) and f(x?,y) ду

A:

Q: II. Let U = R, { x € R | 26x + 25x = 0}, J = { x €R | |4x + 2| > 10 } and K = { x € R | x? – 3x – 4…

A: