If $f(x+y) = f(x)+f(y)+x^2y+xy^2$ and $\lim_{x\to0} \frac{f(x)}{x}=1, (x,y \in R)$, find $f(0),f'(0),f'(x)$
71127
How do I find $f(0)$, $f'(0)$, and $f'(x)$ given $f(x+y)=f(x)+f(y)+x^2y+xy^2$ and $\lim_{x\to0}\frac{f(x)}{x}=1$?
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
48154
Find the minimum value of $f(x,y,z)=\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+z)(y+x)}+\frac{z^2}{(z+x)(z+y)}$.
11707
If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$
38804
Wrong Wolfram|Alpha limit? $ f(x,y) = \frac {xy}{|x|+|y|} $ for $(x,y)\to(0,0)$
12375
Prove $\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0$
129011
Is there limit $ \lim_{(x,y) \to (0,0)} \frac{x^3}{x^2 + y^2}$?
78921
Multivariable limit $\lim_{(x,y)\to (0,0)} \frac {x^2 + y^2}{\sqrt{x^2 +y^2 + 1} - 1}$
10428
Proving that $\lim\limits_{x\to\infty}f'(x) = 0$ when $\lim\limits_{x\to\infty}f(x)$ and $\lim\limits_{x\to\infty}f'(x)$ exist
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
77071
Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$
44060
If $\lim_{x \to +\infty} f'(x) = L$, then $\lim_{x \to \infty} \frac {f(x)}{x} = L$
10068
$f(x,y)= e^{-\frac{1}{x^2+y^2}}$ when $(x,y)\neq (0,0)$ and $f(0,0)=0$.
101130
How to determine the limit of $ f(x, y)=\frac{9xy}{x^2 + y^2}$?
88782
Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$
9746
Determine the following limit as x approaches 0: $\frac{\ln(1+x)}x$
76580
If $f(\frac{1}{n})=0$ all $ n\to \mathbb{Z^{+}}$ then find $ f'(0)$?