True or False: $\lim_{x\to a}C=C$ assuming that the limit exists.

True or False: The limit of a function exists if and only if the left-hand limit is equal to the right-hand limit.

True or False: The limit of a function exists if and only if the left-hand limit is greater than to the right-hand limit ?

True or False lim_x→a​[(f+g)(x)]=lim_x→a​f(x) + lim_x→ag(x) assuming that these limits exist. 

True or False : lim_x→a​[(f-g)(x)]=lim_x→a​f(x) - lim_x→ag(x) assuming that these limits exist.

True or False: _{$\lim_{x\to a}\left[c.f\left(x\right)\right]=c.\lim_{x\to a}f\left(x\right)$} assuming that the limits exist and c is a constant

True or False: The limits of functions sometimes do not exist

True or False: assuming that these limits exist.

True or False: $\lim_{x\to a}C=a$ assuming that the limit exists

True or False: $\lim_{x\to a}\left[\left(f.g\right)\left(x\right)\right]=\lim_{x\to a}f\left(x\right).\lim_{x\to a}g\left(x\right)$ assuming that these limits exist.