(1) Which interval is the real number t in such that A = -1 0 4 2t 0 2t 4 is positive definite?

Q: Let a = 3/2 + 34. (a) Compute a³ and write it in the form pa + q where p and q are integers. Use…

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Q: (a) For every integer n, the number n² — n must be even. (b) For all real numbers a, a² < a¹. (c)…

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Q: from x = 2 to x = 10 and x; is any value of x in Ex¡. Express lim s as a definite integral. n-x n D…

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Q: 1. Find the Laplace transform of the function f(t) = eat[a cos(Bt) + b sin(3t)].

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Q: Let 7 be a real number. Which of the following is equal to T T -2 (ED)*+E)* r2 3 0 None of the these…

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Q: (a) Explain with cases why, if a is a real number,  then a ≤ |a|. (b) Explain, if, for any real…

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Q: (c) Prove that r| +11 36 T-1 2 +36 for all real I.

A: We have to prove that the following inequality holds: x-11x2+36≤x+1136 for all real x. We will use…

Q: Veridy that the approximate root of xa2 is: 1+Xn- Xn 2

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Q: A8. (a) State (without proof) the Intermediate Value Theorem. (b) Use the Intermediate Value Theorem…

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Q: b) Prove that |x| ≤ 1 implies that |x² + 2x - 3| ≤ 4|x − 1].

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Q: X4 none of these X (c) f'(x) does not exist.

A: f''(x) = 0  at sharp corner f'(x) does not exist for f'(x) = 0 , tangent line is horizontal

Q: Prove that for all positive real a we have 22 +5 20x4 2 4/5. 24 x2 +5

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Q: Let A = {x € R : x < a} and B={x €R: x < b}, where a and b are real numbers. Show that sup(A+ B) =…

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Q: The numerical value of xe dr is

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: (c) Let n be a positive integer and assume that there are integers a and b ab. Show that a < yn or b…

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Q: Using the Root Test 12. (in (² + 4))***

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Q: Let a and b be non-negative real numbers with b+ 0 and p,q > 1 and+= 1, then a show that ab <+

A: Define a function y : [0,∞)→ℝ by yt=1q+tp-t1p, for every t∈ [0,∞). Now differentiating,…

Q: 2. Find the Laplace transform of the function g(t) = (1+t+t + t³ + + tm-1 +tm)et.

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Q: [1 2] 1: Let A = 3 2, and B = 10 [2 0 1 0 2 -1 a) Find A B b) Find B. A c) Find AT +3B

A: Explanation of the answer is as follows

Q: Prove that if |x-1| < 1, then x² - 2x + 5| < 8.

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Q: (c) Prove that x - 11 |x| + 11 |x² + 36| 36 for all real r.

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Q: If a, b, c are non-zero real numbers, then bc ca ab ca ab bc vanishes, when ab bc ca ca 1.1 -+- 0…

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Q: Find the value of a such that (3 + 4i)(1+2i) (1 + 3i) 9 = = = q(1 + i).

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Q: Ex if 7- 5+3i find conjucad f z and madulus and argumend of

A: Given:- Z =(5+√3i)/(√3+2i)  To find:- Conjugate , modulus and argument of z

Q: Find all the values of z for which 1+z 1 1 1 1 1+z 1 1 1 1 1+z 1 1 1 1 1+z <= 0.

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Q: Q. No.3 (a) Show that v5 is an irrational number. (b) Let x and y are two irrational numbers. Then…

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Q: (-1)"+1 1- 2n Given the set A = The infimum of A is

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Q: If xER then |1– x| = |x+1|- True O False

A: We have check given statement is true or not

Q: What is the domain of { (z,3z2- 5) Iz ER except 0}? All real numbers All negative numbers {x\x€R>0}…

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Q: Question 1. (a) Prove that for z, w = C, Re (zw) = |z||w| if and only if z = sw for some positive…

A: a)  suppose that the complex numbers are   z=a+ib and w=c+id .  Then we see that w¯= c-id  we see…