Suppose that ƒ is continuous in [0,1] and that f(x) E [0, 1] for all x. Show that f(x) = x for some number x.

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Q: 11)For what value of 'x', the expression x - 5x + 6 is poS A) x 3 B) x > 2 and x 4 and x 3

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Q: Example 2: Using the False Position method, find an approximated root of the function: f(x) = x² – 1...

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on [a...

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A: The general form of a second-order linear homogenous differential equation is given by ay''+by'+c=0,...

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Q: 2. Prove that if m and n are integers and mn is even, then m is even or n is even.

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Q: tet r and m be integer, prove that 17/20+3m iff, 17/9n

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Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then bos nogo 2i (i) Fr(A) = A n (A)° A –...

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Q: 32. Construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible.

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Q: 2 31-1 0] 0? 1. What is the dimension of the null space Nul(A) of A = 0 0 0 0 0 %3D

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Q: Find the Laplace transform of the given function: f(t) = (t – 7)us(t) – (t – 4)u7(t), where uc(t) de...

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Q: 4) If x and y vary inversely, and x = -3 when y = 1/3, what is y when x = 9?

A: If x varies inversely with y yα1x y=k1x put x=-3  y=k13-------(1) from our given y=-13------(2) comp...

Q: 2. Given the data 0.2 0.4 0.6 f(x) 1.9934 2.1465 2.2129 2.1790 0.8 1.0 1.2 1.4 f(x) 2.0683 1.9448 1....

A: We can solve this by using given data and formula of Central difference

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Q: Consider the following recursively defined sequence: 5 an+1 = 2' 1 - (а, + 2), п € N. aj = 1 Prove t...

A: Given sequence is  a1=52,an+1=12(an+2),n∈N To prove  an>12n ∀n∈N