If $\lim_{x \to c} f(x)$ does not exist and $\lim_{x \to c} g(x)$ does not exist, then $\lim_{x \to c} (f(x).g(x))$ does not exist.
90471
Can the limit of a product exist if neither of its factors exist?
102478
$X_n\leq Y_n$ implies $\liminf X_n \leq \liminf Y_n$ and $\limsup X_n \leq \limsup Y_n$
127125
Can the limit $\lim_{h \to 0}\frac{f(x + h) - 2f(x) + f(x - h)}{h^2}$ exist if $f'(x)$ does not exist at $x$?
120777
How to formally prove that if $\lim \limits_{n \to \infty}a_n=\infty$, then $\lim \limits_{n \to \infty}\frac{1}{a_n}=0$.
15579
Show that $f$ is uniformly continuous if limit exists
48464
If the derivative approaches zero then the limit exists
40870
Sequence Limit Problem: If $0 \leq x_{m+n} \leq x_n + x_m$ then limit of $x_n/n$ exists
80720
What paths to choose to prove that $\lim_{(x,y) \to (0,0)}\frac{xy^2}{x^2 - y^2}$ does not exist?
98377
How can I prove this limit doesn't exist?
60498
Prove that $\lim_{(x,y)\rightarrow(0,0)} \frac{|x|^{a}|y|^{b}}{|x|^{c} + |y|^{d}}$ does not exist
86458
Choosing $2$ paths through $(0,0)$ to show: $ \lim_{(x,y) \to (0,0)}\frac{xy^2}{x^2 + y^4}$ does not exist
20404
Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$
121217
How to show that $\lim\limits_{x \to \infty} f'(x) = 0$ implies $\lim\limits_{x \to \infty} \frac{f(x)}{x} = 0$?
47381
If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
21670
Why does an infinite limit not exist?
44336
Is $\lim\limits_{x\to x_0}f'(x)=f'(x_0)$?
111290
If $f$ continuous and $\lim_{x\to-\infty }f(x)=\lim_{x\to\infty }f(x)=+\infty $ then $f$ takes its minimum.