Question 28
Let $p$ be a real number and $c \neq 0$ an integer such that
$$
c-0.1 \lt x^{p} \left( \frac{1-(1+x)^{10}}{1+(1+x)^{10}} \right) \lt c+0.1
$$
for all (positive) real numbers $x$ with $0 \lt x \lt 10^{-100}$. (The exact value $10^{-100}$ is not important. You could replace it with any "sufficiently small number".)
Find the ordered pair $(p, c)$.
$$
c-0.1 \lt x^{p} \left( \frac{1-(1+x)^{10}}{1+(1+x)^{10}} \right) \lt c+0.1
$$
for all (positive) real numbers $x$ with $0 \lt x \lt 10^{-100}$. (The exact value $10^{-100}$ is not important. You could replace it with any "sufficiently small number".)
Find the ordered pair $(p, c)$.