If a z 0, then |a If a < 0, then |a||

Q: if A) B) none of these a(n) a(n) is smaller or equal to oo then is finite

A: In the question we have to select correct option.

Q: If f(x) = and g(x) = z+3 %3D I-1 H-2 The domain of fogis the set of all real numbers except z+1

A: For f(g(x)) to be defined first g(x) needs to be defined

Q: Let f:A-B and X,Y be subsets of B. Then f-¹(XnY) = f'(X) nf-¹(Y). True False

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Q: a) f'(c)=0 b) f"(c) is either zero or undefined c) If f"(c) is defined, then it is positive. d) If…

A: Given query is to find the correct statements.

Q: Determine the interval(s) on which x2 + 2x – 3 > 0. - Ох1 Ox 1 -3 1

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Q: 2 а ху Let A = and A-= -1 Then x + t - z is equal to z t O -1/2 O none of these O a/2 O 1/(2a) -a/2

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Q: B = {1 + x + x, x + x2, x2}. for P2. Let p(x) = 2+x + 2x?. Then [p(x)]3 : %3D %3D 2 - 1

A: Using linear combination of three polynomials

Q: Determine a and b such that p(x) = x2 + ax + b satisfies p(1) = 0 and p ,(1) = 4.

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Q: Find real numbers x and y such that ty 2 2 - i i+3 1 +1

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Q: 27. Let f(x)= [x²/3]. Find /(S) if a) S-2, 1, 0, 1, 2, 3). b) S= (0, 1, 2, 3, 4, 5). c) S = (1,5. 7.…

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Q: A factor (x − a)k, k &gt; 1, yields a ________ ________ x = a of ________ k.

A: x=a is a repeated zero of multiplicity k, when we have (x-a)k.

Q: If n is any real number and f(x) = x", then f'(x) = nx"-!

A: Why does ddxxn=nxn-1                 ddxfx=limh→0fx+h-fxh…

Q: Find a number a + 5 such that S" (1 – æ) dæ = 0

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Q: Using the Mean Value Theorem, we can prove that a. 2* > 1+ xln2 for all x > 0 b. 2* 0 c. 2* =…

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Q: Let x and y be postive numbers such that x+2y=50. Fing the values of x and y that make the quantity…

A: Here we will use the concept of maxima and minima to solve this question

Q: Let a, b eR with a < b. Assume that a + <b - for all n e N. Show that n n=1

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Q: Let f(x) = and I =]1, 00[. Then for all x, y > 1, -1 3+Vx X-y is less than 1/64 None of these is…

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Q: Q4/ Let S(x)=- x-1 S(x)= and g(x)=1+ Find (g(x) and ag)(x).

A: We define two functions: f(x) = x/(x - 1)  g(x) = 1 + 1/x = (x + 1)/x Then, we have to find the…

Q: For what value of a, m and b does the function { 3 x = 0 -x2 + 3x + a 0 < x < 1 1< x < 2 g(x) = mx +…

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Q: TRUE/FALSE If A = A−1, then A must be equal to either I or −I.

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Q: If F(s) : then (s-1)² '

A: This question is related to Laplace transform

Q: Ex let x be with pmf 1=,2,3, 16 O find c P(X)2)

A: We want to find the value of c and P(X≥2) and P(X2=9)= ?

Q: Let h(x) = -3) Then, h(x) has a zero on (0, o). —1) (ӕ+2)(2+3а) O True False

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Q: A. Evaluate the follow 1. S dy 3+√y+3

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Q: f(x) = In (1+x³)

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Q: 1. Suppose f: A B and W and X are subsets of A. (a) Will it always be true that f(W U X) = f(W) U…

A: We are given that f: A --&gt; B and W and X are subsets of A. For (a), The given statement f(W∪X) =…

Q: 2. Let f(x, y) = (2x – y,x – 2y); (x, y) E R × R, (R is set of real numbers.) a) Show that fis one…

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Q: Let X = n(u,4) and Var(2x) = E(4–7x) find u.

A: As per our guidelines we are suppose to answer first question .

Q: If x and y are both less then 0 and xy

A: Given, x and y are less than 0. Then xy = ?

Q: If g(y) is differentiable for 2 < y < 3 and g(2) = g(3) = –-1, then there is some 2<a< 3 such that…

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Q: 1. Show that if f: [a,b] → R and a < xo <b, then f'(xo) exists if and only if D f(x) = Dƒ(x) € R.

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Q: Let n be a positive integer, then n+1≥ for all n.T/F

A: We need to show that n+1≥n for all n where n is a positive integer. Lets proof by contradiction

Q: Suppose that the functions s and t are defined for all real numbers x as fe s(x) = 2x+1 t(x) = 6x…

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Q: -{ x² – 2, x + 4, x 3 false true

A: Let's find.

Q: (ii) For what values of a, m and b does the function x = 0 0 < x < 1 3 f(x) : -x² + 3x + a тх + b…

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Q: B = {1 + x + x², x + x², x²}. for P2. Let p(x) = 1 + 3x + 2x². Then [p(x)]B = 2 of 2 1 None 1 2

A: The given set is: B= 1+x+x2, x+x2, x2

Q: Find all values of x for which rank(A) = 2. -1 2 0 5 A = 2 -2 x -3 -1 4 6 12 x =

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Q: Is it true or fase ? There is a number c in the interval (a, b) such that f(c) = 0.

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Q: Let a, x, and y be real numbers and let e > 0. Suppose that |x-al < e and y-al <e Use the Triangle…

A: Given that, a, x, and y be real numbers and let ε &gt; 0Also,x-a&lt;εand y-a&lt;εWe know…

Q: Using the Mean Value Theorem, we can prove that a. 2* > 1+ xln2 for all x > 0 b. 2* 0 c. 2* = 1+…

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Q: Let f (x) = -2r, de fined on -1, 1], then L (P ) = 2 (n– 1) 2- 4 (n+1) 4 (n – 1) 4 (п-1) 2n2

A: We need to find the lower Riemann sum

Q: If f(x)=3x+x-4, f(x) satisfies the hypothesis of Mean value theorem on the interval [1,5].Find a…

A: We have to find c

Q: Let a, b e R with a < b. Assume that a + <b - for all n E N. Show that 1 = (a, b). a + ,b n n=1

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Q: B = {1 +x + x², x + x², x²}. for P2. Let p(x) = -1 + x + 2x2. Then [p(x)]B = 2 None 1

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Q: 2. (2) Let f : R" → R. Suppose that given any e> 0, there exists r E R" such that f(r) <2+e. Prove,…

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Q: ? Suppose that * f(3) = }, and f(x) > 0, and f(x) < 0. Is it possible that Í(2) = . 3 O False True

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Q: 1. Let x, y, and z be real numbers. Prove the following: [a] -(-x)= x [b] (-x )y = -(xy) and (- xX-…

A: Here you go. Just use a square property and answer follows.

Q: Let x and y be positive numbers such that such that x + 2y= 50. Find the values of ? and ? that make…

A: Please refer the attached image for complete solution.

Q: 50. If f'(x) = In(x²) and f(5) = 8, then f(3) %3D %3D

A: Given : f'x = lnx2f5 = 8