MathDB

2015 Algebra #3: Basically Limits

Source:

March 28, 2015

algebralimits

Problem Statement

Let

p

be a real number and

c\neq 0

such that

c-0.1<x^p\left(\dfrac{1-(1+x)^{10}}{1+(1+x)^{10}}\right)<c+0.1

for all (positive) real numbers

x

with

0<x<10^{-100}

. (The exact value

10^{-100}

is not important. You could replace it with any "sufficiently small number".)
Find the ordered pair

(p,c)