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

 

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}​