If f(z, y) – e . In(9y) , then fz is given by: O - 9e In(9y) o - 27 e In(9y) O 9 e In(9y) O 27 e In(9y) 3z 3z

Q: 3. Consider f (x, y) = a +6V-10. Compute the following: (a) (b)

A: Given,          fx,y=x4+6y-10

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: 1. Show (in terms of e- 6) that a function f : R* → R defined by f(x, y, 2) = (2x + 3y + 42) is…

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Q: In GF(2), find the inverse of x^3+x+1 modulo x^5+ +x^2+1. Show your complete sölution Oax^3+x…

A: For some finite field  F and fx ,gx∈Fx s.t gx≠0 On applying successive division algorithm:…

Q: Let f(x, y) = xcosy- y e*y. fry at (1,0)is equal to: -5 3 -1

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Q: 2.2 If fe R(a) on [a, b] and if Saf da prove that a must be constant on [a, b]. = 0 for every f…

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Q: If L(x)=mx+b is the linearization of f(x)=2x³ - x +3 at x-1, then m= Using L to approximate 2(1.01)…

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Q: Evaluate SSS 7e(=²+y²+z?)*² dV over B where B = {(x, Y, z) : x² + y² + z² < 1}. Take T = 3. Turkcen.…

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Q: a Oclvmina f drz saby Couchy- Reimon Sabisty couchy- Reimon "qualior andlgove fl © frz> = g-2xy ti…

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A: We have given geometric distribution and two statistics associated with it and we have to check…

Q: 4. Define f: [0, 1] → R by if x E Qn [0, 1] if x ¢ Qn [0, 1] f(x) = (a) Prove that S° f = 0; s*f =…

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Q: {o, c, s}. Find two values of c in (0, 5) such that Uf (P) = 21. %3D Let f (x) = x on [0, 5], and…

A: Given : f(x) = x on [0,5] Partition of the interval P = {0 , c , 5 }. Uf(P) = 21

Q: Given g(z)- In(8z +z), the derivative g(z) is %3D O 8z + O 9z O 72z +1 7278+1 O 72r +1

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Q: Let z = a?y- ay?, x = e-24, y = e*, then which of the following is at O a. 2e-2t – 2e2t O b. 2e2t –…

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Q: Find f"() if fx) = 2e* - %3D e* In 2 Ob) 20 2e* O c) 2e O d)

A: Recall:     d(eax)dx=a.eax

Q: f: [o,17 s R. )m =l,2,3, fcx) = 3. otherwise Prove that f t R[O,1]

A: The given function is f: 0,1→Rwhere f(x)=1 if x=1n,n=1,2,3,...0 otherwise

Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: Let f(t,y) = y+ 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1sts2.…

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

Q: The ODE M(z. v) dz + N(z. v) du = 0 is exact if and only if

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Q: (a) Let a > 0. Using the substitution t = In x or otherwise, prove that In a e 4/a² - e 2t dt =a5…

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Q: 3. If f(x, y, z)= In xyz te(3.0²), find f,,f, and f-· 4

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Q: Let f(2)=³ and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of Ac…

A: Given that             fz=z4-5z2      and    C=z∈ℂ : z=1.

Q: -2 Let f(t,y) = y + 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1<t<2.…

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Q: 1 1 Prove that: L' a exp(a't) erfe( avt), where erfc is complementary a+v error function.

A: Formula Used:- L1t=πsLeat=1s-aLerf(at)=as(s+a)Leatf(t)=F(s-a)                   where…

Q: Evaluate f (22 -1)(z2+3z+2) O a. 구미z+11+ + 흡nz-1-mlz + 21 +C ㅇ b. 글mle+11 + 1 + 습nz-11+ 옮mlz+ 21 +C…

A: Solving the problem by finding the integration.

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

A: We have to choose the correct answer from the given options according to the given information

Q: o prove that knVA=| Test the seuence (ConViordív) of (10) an = (^_-) ) an 15 ら 9n: 3ntl 3n-1 (の+ (7)…

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Q: 4. Evaluate both sides of Green's theorem, for: F = (-x²y,xy²) where C is shown in the following…

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Q: Q: If f(x)= ax* + withE a, > 0, b >0 +b,x + b, then show that Lt f(x)=o ifn>m. %3D

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Q: If f:(0,∞)→Rf:(0,∞)→R is defined by f(x)=xln(2x)f(x)=xln⁡(2x) for every x∈(0,∞),x∈(0,∞),  then…

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Q: In ΔFGH,  FH is extended through point H to point I, m∠FGH=(x−2)∘,  m∠GHI=(4x−5)∘, m∠HFG=(x+19)∘.…

A: Given that     FGH is triangle. FH is extended through point H to point I .

Q: /et A 3 8 カー (-45 Show That LA+B S ZA+B) 3-5 = At B

A: Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given…

Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

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

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Q: If f(t)dt = 1, S g(t)dt = 3, evaluate (3f(t) + 2g(t) – 5)dt.

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Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: If utt 4ura u(x, 0) = e", u4(x, 0) = 0, u, Ux → 0 as x → ∞, then u e* cosh(2t) O e2 cosh(4t) O e2¤…

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Q: If f(x) = x(e*+) , then f'(x) = %3D (A) (e + x³) x(e²+x²-1) (B) (e" + 5x*) In(x) æ(c*+z*) (C) (e* +…

A: To find f'(x) for the given function

Q: 10. Show that S t2 if 0 1, 2(1 - e-) then Ldf %3D

A: Laplace of differential equation.

Q: Given that X has pmf f(x)=1/(2)^(x+1) , x=0,1,2,... and et<2 , use mgf technique to…

A: Given: X has the pmf as follows, f(x)=1/(2)^(x+1) , x=0,1,2,...et&lt;2

Q: What is G = xy ax – x²y ay + 2y az at B(3, –4, 1), expressed in SCS? 36.8698а, — 14.9048аg + 12аф -…

A: Please check step 2 for the solution.!

Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 fx) =4x

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Q: • In z Find F" (2) if F(x) et dt a² _4 O A. 1 O B. 0 Ос. -2 O D. -4 O E. –3

A: Given:         Fx=∫x2-4ln xet dt                 =etx2-4ln x                 =eln x-ex2-4…

Q: he joint pmf of X and Y is given below. What is E()XI-M)? Y -1 1 X 1/16 1/16 1/16 1/8 1/16 1/8 1/8…

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Q: H. If g(z) e2*z In , compute g'(r). What techniques should you be using in this %3! case?

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Q: Given G(x) = jin(2t+1)dt , find G '(x). O In(2x + 1) O In(2x + 1) - In3 O In(2t + 1) + C 2 2x+1

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Q: 3. If f(x) = -x, g(x) = 2x + 1 and h(x) = x2, find fogoh 1 point %3D %3D О А. х2 - 1 О в. 2х2 - 1 О…

A: We use fogoh=f(g(h(x))).

Q: Prove that (A')' = A for each A E Mmxn(F).

A: