15. Given: DE ||FG || ĦJ Prove: DF GJ = FH·EG E F G H

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Q: Exercise 2. * Let f(z) Fa- and C: Iz – 9| = 1. Then f. f(z)dz = sin(32) a. 0 b. 2ni c. 9 d. None of…

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Q: xsiny If f(x.y,z)3D then fy 23 b. False xcosy 23 a. True

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Q: 1. Let A = a b c def ghi B ba bb b c gh i de f If de+ (A) = -1/24 then what is det (B-¹)? and AUT

A: Square matrix: If a matrix A has the number of rows equal to the number of columns. Then, the matrix…

Q: If f(x) dæ = 0 where a < b, a, b ER, then f(x) = 0. a

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Q: Evaluate the following definite integral: **12sin³xcosxdx O O a.) b.) d.) П S 3 12sin³xcosxdx= 16 П…

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Q: Let a A = d e h i and -3a -3b -3c B = g h i d e f Given that det(A)=1/15, what is det( B¬l)? Answer:

A: Just I have used the property of determinant of a matrix. (1) if two rows of determinant are…

Q: hort proof. 5. Show that cot 0 d0 is equal to In|sin 0| + C.

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Q: Assume that d and e are constants and, 3 - f, if f <1 ) = { df²+ef. { z(f) = if f < 1

A: I am going to solve the given problem by using soem simple calculus to get the required result.

Q: Find F.T [e-t sin(wot)u(t)]

A: Given Data: The given signal is e-tsinw0tu(t). sinw0t=12jew0t-e-w0t To Find : F.T

Q: J₁³ Let R be the rectangle defined by the inequalities 0 ≤ x ≤ π/2 and 0 ≤ y ≤ π/4. What is the…

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Q: Suppose that A,B⊂S such that Pr[A|B]=3/7, Pr[A]=3/10 and Pr[B′]=13/20. What is Pr[B|A′]? Write as a…

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Q: Find nd [[ cos (2² +3³)dA where D = { = {(z,y) | 4 ≤ x² + y² ≤ 36}

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Q: Exercise 1.3.5. Verify (by tedious computation or Maple) the following formula known as Lagrange's…

A: Consider the provided question, Exercise 1.3.6: We have to prove that v×w=vwsinθ by using the…

Q: Xi Xn XENGI De)since Xisthe mde for G, and Ś is the m-L.efor @2Then? X+25isthe miLe for @l+2v@z

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Q: af and If f(s, t) = t sin st, find - as at

A: Given,          fs,t=tsinst

Q: Q1. Solve the following: of A. Iff (u,v,w) is a function and u=x-y, v= y-z and w=z-x. Prove that…

A: A) To prove: ∂f∂x+∂f∂y+∂f∂z=0 Given that u=x-y, v=y-z, w=z-x

Q: r r 2r p 2r 3r p 2r 3r 4r .. .. .. m 2m 3r nr Show that S 1 and 0 < r < 1. [Hint: E, iri < (1-r)²…

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Q: onsider the function w = f(x,y), where x = rcosθ and y = rsinθ. Verify each of the following. a.…

A: Given w=f(x,y) Let us substitute x=rcosθ, y=rsinθ in w. w=f(rcosθ, rsinθ) To find the partial…

Q: Use the Squeeze Theorem to show that lim a sin (1/r) = 0. Show all %3D work. 2.

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Q: Q47. If I = √√√1 + cos x dx, then the domain of I is?

A: First we integrate and then find the domain of I

Q: Q.3 Evaluate the by using the appropriate u –sustitution. cos (ln x) dx

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Q: Evaluate Jo F. dr where F= (-z, y, 4x), and C is given by r(t) = (sin(t), t, cos(t)), 0≤t≤T.…

A: I have explained everything with in the solution. Please go through that.

Q: consider the function f, such that f(x) = (ax + 3) * e*. If the slope of the tangent line to the…

A: Topic = Derivative

Q: How do I prove this?

A: Consider

Q: Q1: Choose the correct answer Let X haveN (u, o²), then 3. The value of E(x-μ|²) is O A B A. 0² B.…

A: Solution Given X~N(mu,sigma^2)

Q: 2. Prove that, for all r ER, | sin x ≤ |r|.

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Q: 7 T 5 r Evaluate: |||sin0 dz r dr d0 0 0 0

A: We have I =∫0π∫05∫07rsinθ dz r dr dθ⇒I =∫0π∫05∫07rr sinθ dz  dr dθ

Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: -3 Vennty that A 3. 2. Varities Caley tHownilton theorem

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Q: sin(3z) Let f(z) = and C: |z – 9| = 1. Then ſ. f(z)dz = %3D z?(z-n) a. 0 b. 2ni с. 9 d. None of the…

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Q: D. O D. Z14

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