Let f : [0, 1] −→ [0, 1] be continuous. Use the Intermediate Value Theorem to show that f(x) = x for some x ∈ [0, 1].

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Let a and b be real numbers with a < b. Suppose that f : [a, b] −→ R is continuous and that f is differentiable on the open subinterval (a, b). Use the Mean Value Theorem to show that if f ′ > 0 on (a, b) then f is strictly increasing on [a, b].

Write down any three specific nonzero vectors u, v, w from R 3 and any two specific nonzero scalars a, b from R. Compute u+v, aw, b(v+w), (a+b)u, u + v + w, abw, and the additive inverse to u.

Simplify - 8/19+-3/57

Divide segment AB of length 7 cm into a ratio 3:2

What is the percentage decrease in an interval containing root after iteration is applied by Bisection Method? 30% 40% 50% 20%

The cost price of 25 articles is equal to the selling price of 20 articles. What is the gain or loss percent?

If A+B=, [2/3 3/0] and A-B =[5/2 3/1] then Matrix A is

6⅔ find the factor.

If A {x:x is a factor of 42 } B = {x:x is a factor of 54} Then find AUB, AnB, A-B and B-A.

Write the power set of the following set B={x,y,z}

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