Prove: e is an irrational number. the following is an outline of a proof: (a) use the taylor formula to show 0 < e − 1 + 1 1! + 1 2! + 1 3! + + 1 n! < 3 (n + (b) assume to the contrary that e is rational, say, e = a b , where a and b are positive integers. pick n > b and n ≥ 3. substitute e = a b into the inequality in (a) and multiply the inequality by

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2

answer: 819.89 miles across america

step-by-step explanation:

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a

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answer