1. Let A=(a)xn be symmetric and positive definite. Show that a) a>0, i=1,2,...,n. |a|< (aa)², i, j=1,2,...,.

Q: i. If n is positive integer, Find (√3+ i)” + (√3 − i)”. ii. Separate tanh-¹(x + iy) into real and…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 9.) Consider the function f (x) = x? – 2x – 1 for x € [2,4]. Use n = 10 to compute accurate to 10…

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Q: 3.) / sect 0 do

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Q: 2. Show that by using MEAN VALUE THEOREM . u-v < tan-1 v - tanu < if 1+v2 u-v 1+p2 0< u<v and ded…

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Q: Refer to the figure to determine f'(a) for a = 1, 2, 6, 8. y 5- 4 3+ 2- 1- 1 2 3 4 5 6 7 8 9 (Give…

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Q: 14.Let A= 3+2i 0 2 1+i 1-i B-( + ?) and B= Find AB.

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Q: Let X-(1,0,-1,-V2)'. Then, |X|l2= Select one: a. 2 b. 1 C. 3

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Q: 3. Determine a and b for Y X1 and Y2aX bX2 such that EX1 EX2}= 0, Var(X) Var(X2) Var(Yi) Var(2) 1,…

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Q: Let v = [1] and let z = [¹] x The Projx is equal to k k [21] where

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Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

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Q: EN: Find a) zo value if P(Z > zo) = 0.7 b) P(-1.37 < T < 2.36) when v = 10 c) x² if P(x² < X² < 22)…

A: The question is about continuous prob. distributionIntroduction :Std. normal dist. : is a std.…

Q: (B1>0 (g) If a > b and c> d, then a + c > b + d. h) If a > b> 0 and c > d > 0, then ac > bd. i) If a…

A: For (f) ,We use a theorem that "if n∈ℤ and n≠0 then n2&gt;0.

Q: (a) Use the first two digits as the stem. Then order the leaves. Provide a label that shows the…

A: The data is given on the winning scores of the conference championship games. Sample size (n)= 35

Q: (1) Let x, y E R be positive real numbers. Then: a) 3n EN3 x< ny. (b) 3neN 9 0< < y. (c) 3n…

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Q: For each statement, either prove that it is true or come up with a counter example N(ATA) = N(A) ● •…

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Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: 1. Let f: ZZ be defined by f(x) = -x for all x € Z. Is f injective?

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Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

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Q: prove that l+2 +3+.. +h = n(ntl) for n=1,2g3 2 %3D

A: Given :               1 + 2 + 3 + ... + n = n(n+1)2 Let P(n) :               P(n) = 1 + 2 + 3 + ...…

Q: Let a bc A= d ef g hi Assuming that det(A) = – 7, find a) Det(2A) b) Det(A´') c) Det(3A') d)…

A: Given that: A=abcdefghiand det(A)=-7

Q: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

Q: Using DeMoran's thearem, show that: L (A + B)'(.4' + B')' = 0 b. A + A'B +.4'B' - 1

A: Concept: a. Given; A+B'(A'+B')'=0 We shall solve the Left hand side of equation. Apply Demorgan's…

Q: S # 3 X Use the fundamental Identities to simply the expression. 1) tan & coft 2) cos²0 2 +CSCO sint…

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Q: Find the distance between 4y + 3x = 4 and point (0, 5) O 3.4 O 3.2 O 2.8 3

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Q: Evaluate y ds, C: x = t², y = t, - 1<t < 9 |3D (325)-(5)를 1 12

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Q: let v = (1, 2, 4), u = (6, −1, 2), and w =(1, 0, −3). Calculate the given quantity.  v · (u × w)

A: v=(1, 2, 4)u=(6, 1, -2)w=(1, 0, -3)

Q: Prove tan-lz = Prove tan z= -j In j-z'

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Q: Let f1, f2, .. fn be n real-valued, differentiable functions.- Prove that e :[fif2 ... fn] = (fif2…

A: We have to prove that the given formula.

Q: 41. For ), find all values ofx and y such thatx,y)=0 simultaneously. and yr.y)=0 f(x, y)…

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Q: Let X=(1,0, – 1, - V2). Then, ||X||1= Select one: a. -1-V3 b. C. -/3 o d. 2+V2

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Q: A₁ Let 2 + sinh (2²) - ₁₁ = 27 where w = f (x, y, z)- 1 पुर Find aw дх Jw and Iw > zw. ay dz 3/20

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Q: Let X- N(10, 5'). What is P(X > 3)?

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Q: For any natural number m, evaluate 1/m +x")( 3m 2m 2m +x 2x +3x" +6)"* dx, x > 0. m X

A: Topic:- Integration

Q: 1. A voltage V being supplied to an electrical circuit at time t is V=100sin50++50sin100+. Find the…

A: We have to find the maximum and minimum values of V over one period.

Q: The area of the segment of a unit circle, A is A = ²(0 - sine) where 0 is in radians Dotorming A if…

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Q: Let X=(1,0, – 1,-V2)'. Then, ||X||2 = Select one: а. 3 O b. 4 C. 2 O d. 1

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Q: 10. The interval for |(z )/5-1|<1 is Oa. [0,10] Ob. (0,10) Oc. (0,2 ) Od. [0,2 ]

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