Find $f(x) = x + \frac{2}{3}x^3 + \frac{2\cdot4}{3\cdot5}x^5 + \frac{2\cdot4\cdot6}{3\cdot5\cdot7}x^7+\cdots$ where $|x|<1$
124440
Evaluate this power series
76990
Find $\lim_{x \to - \infty} \left(\frac{4^{x+2}- 2\cdot3^{-x}}{4^{-x}+2\cdot3^{x+1}}\right)$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
127558
If $f(x)=x-\int^{\frac{\pi}{2}}_0f(x)\sin(x)dx$ find the explicit function for $f(x)$ in its simplest form
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
19355
prove $f(x)=x^3+x$ is one to one and onto
82024
If $f(x)\cdot f(f(x)) = 1$ for all $x \in \mathbb{R},$ and if $f(10) = 9$ then find the value of $f(5)$
106013
Given $f(x) = x + |x|$ for what values of $x$ is $f$ differentiable
117353
Polynomial equation $f(x)f(2x^2)=f(2x^3+x)$
53116
How find this sum $f(n)=\sum_{i=1}^{n}\dfrac{\binom{n}{i}}{i}$
74718
Find remainder when $f(x^{12})$ is divided by $f(x)$
124629
If $f(x) = \frac{4^x}{4^x+2},$ find the value of $\sum \limits_{i=1}^{1999} f\left(\frac{i}{1999}\right) $
132093
Solve $f(f(x))=f(x)$
76580
If $f(\frac{1}{n})=0$ all $ n\to \mathbb{Z^{+}}$ then find $ f'(0)$?
136655
Find the range of the given function $f$
147184
$f:[-1,1]\to \mathbb{R}$ is a continuous function such that $f(2x^2-1)=(x^3+x)f(x).$ Find $\lim_{x\to 0}\frac {f(\cos x)}{\sin x}$
105117
$1 + \frac{1}{3}\frac{1}{4} + \frac{1}{5}\frac{1}{4^2} + \frac{1}{7}\frac{1}{4^3} + ..........$