I NEED HELP FINDING LIMITS ALGEBRAICALLY
lim t^3+8/t+2 ^{t}^{-->-2}
For the first limit, try writing the numerator as the sum of 2 cubes.
For the second, barring the use of L'Hôpital's rule, try writing:
$\displaystyle \frac{\tan(3x)}{\tan(5x)}=\frac{3}{5} \cdot \frac{ \tan(3x)}{3x} \cdot \frac{5x}{ \tan(5x)}$
The first thing you should try, to find $\displaystyle \lim_{x\to a} f(x)$ is calculating f(a). That doesn't work for this problem because both numerator and denominator are 0. And that $\displaystyle t^3+ 8$ is 0 when t= -2 [b]tells/b] you that it has a factor of t+ 2. That is, $\displaystyle t^3+ 8= (t+ 2)(t^2+ at+ b)$ for some a and b. What are they?