Show that is integrable on [0, 1]. f(x) = {1. 0, +√√xsin(1/x6), x‡0 X 0

Q: Evaluate integral of interval 1, 1/2 of (x-3 -8) d x

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Q: Let x, y be real numbers such that xy=1x and x≠y. Prove that x^2+y^2≥2\sqrt{2}|x−y|.

A: Given: xy=1x,x≠y To find: x2+y2≥22x-y

Q: Differentiate the following function 3 U = ²³² √² + ² + 2 u= +2√+³

A: Derivate with respect to t

Q: Show that the entire function cosh(z) takes every value in C infinitely many times.

A: The function cosh(z) is the hyperbolic cosine of z and is defined as:cosh(z)=ez+e−z2We are…

Q: Find the absolute max. and min. of each function y=√4−x^2, (−2,1)

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 1 =dx <1 Prove 4 4

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Q: Decide whether or not the real function In (eon 2) I+0, = (1) 1= 0, is continuous at r = 0.

A: The given function is fx=ln cos2x2x2     if  x≠0-1                if  x=0. Compute the limit…

Q: (d) Prore that the function f(x) =X is Continous but not unifomly Continous on the intenal

A: Use the  absolun delta definition for uniformly continuous

Q: The iteration of the Bisection method can be stop when f'(c.) - 0. False True The Newton-Raphson…

A: As per guidelines, I can answer only three subparts.

Q: If f is a function defined from R to R, is given by f(x) = 5x - 3 then f -(x) is given by %3D -- 20…

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Q: Soluti 03 16. A 11 22 1 Let Ax- b be a linear svstem of n eauations in n unknowns, and assume that A

A: Given: A = 03-2114225, b = 75-2  and Ax = b To find: The value of matrix x.

Q: Show that x + is increasing on [1, 0).

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Q: c) Which of the following functions are analytic in 121² 2 2: 42²26649 (ii) Z²-1 Z-√√Z²74

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Q: Show that cosh x> 1 + x² for all x.

A: comparison

Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

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