Prove that $e^x - \ln(x)=2^{2014}$ has exactly two positive real roots
59160
Roots of a given equation
98344
Prove that $\int_0^1[f''(x)]^2dx\ge4.$
56311
Proving $(1+a_{2})^{2}(1+a_{3})^{3}\cdots(1+a_{n})^{n}\ge n^n$ for positive reals $a_2,\ldots, a_n$ whose product is $1$
141184
Proof that a degree 4 polynomial has at least two roots
88328
Proof of $1+x\leq e^x$ for all x?
15232
Proving an inequality involving real powers
27494
$P_n(x):=1+ \sum_{m=1}^n\dfrac{x^m}{m!}$ has no real root for even $n$ and exactly one real root for odd $n$
126445
Proving the second root of a quadratic equation
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
118916
How do I prove that a polynomial F[x] of degree n has at most n roots
50509
Prove that $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}}~dx=0$ (without trigonometric substitution)
149889
Prove that $|\log(1 + x^2) - \log(1 + y^2)| \le |x-y|$
101289
Studying the equation $\ln(x)- 1+ x^2=0$
39504
Why does $ \frac{2x}{2+x}$ provide a particularly tight lower bound for $\ln(1+x)$ for small positive values of $x$?
91877
Let $|x|\leq1, |y|\leq 1$. Show that$0 \leq x^{2}+y^{2} -2x^{2} y^{2}+2xy \sqrt{1-x^{2}} \sqrt{1-y^{2}} \leq 1$
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
52380
How to prove the function $e^x$ is continous for all real numbers