Find the following limits.

1. $\lim\limits _ { x \rightarrow \infty } \frac { 5 x ^ { 2 } + 2 x - 3 } { x ^ { 3 } + 1 }$

   Hint (a):

   The dominant term is in the denominator.

   Answer (a):

   The limit is $0$.

2. $\lim\limits_ { x \rightarrow \infty } \frac { 2 x ^ { 3 } - 7 } { 3 x ^ { 3 } + 4 x - 5 }$

   Hint (b):

   The dominant term is in both the denominator and the numerator.

3. $\lim\limits _ { x \rightarrow 0 } \frac { 2 x ^ { 3 } - 7 } { 3 x ^ { 3 } + 4 x - 5 }$

   Hint (c):

   You cannot use the dominant term idea for this problem because $x→0$ (not $∞$). Simply substitute $0$ in for $x$.