Real function, satisfying $\frac{\mathrm{d} }{\mathrm{d} x}f(x_0)<1+f^2(x_0)$
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
110219
Bound on the derivative of a holomorphic function at $0$
95288
Prove that, $f'(0) \ge -\sqrt{2}$ for a function $f$ satisfying some conditions on $(-1,1)$.
110093
Proving that the solution to $f^{\prime}(x) = \frac{1}{x^{2} + (f(x))^{2}}$ is bounded above.
16418
Showing that $\frac{f(x)-f(x-h)}{h} \le f'(x) \le \frac{f(x+h)-f(x)}{h}$ given that f' is increasing
103030
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
62524
Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even
157762
Showing $f_n(x):=\frac{x}{1+n^2x^2}$ uniformly convergent in $\mathbb R$ using $\epsilon-n_0$
22153
Power Series of a Holomorphic Function determined by its Real Part and $f(0)$?
60520
Upper bound for $|f(0)|$ based on its behavior within the unit disk.
99894
Does there exists an entire function $f$ such that $f(0)=1$ and $|f(z)|\leq \frac{1}{|z|} $ for all $|z|\geq 5$?
97553
Continuity of $\frac{2xy}{x^2+y^2}$ at $(0,0)$
56958
bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$
120985
Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$
95626
$\int_X |f_n - f| \,dm \leq \frac{1}{n^2}$ for all $n \geq 1$ $\implies$ $f_n \rightarrow f$ a.e.
114047
Metric $d(x,y)=\frac{|x-y|}{\sqrt{1+x^2}\sqrt{1+y^2}}$ on $\mathbb{R}$
12859
Find $\int \frac{x^3}{x^2-1} \:\mathrm{d}x$