The limiting situation in this equation would be the denominator. Plug the value that n is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will equal zero when n=5; so we try to eliminate the denominator by factoring. When the denominator is no longer zero, we may continue to insert the value of n into the remaining equation.

We see that we can no longer factor this to make the denominator not equal; hence this limit DNE because the denominator is zero.

The limiting situation in this equation would be the denominator. Plug the value that n is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will equal zero when n=-1; so we try to eliminate the denominator by factoring. When the denominator is no longer zero, we may continue to insert the value of n into the remaining equation.

We see that we can no longer factor this to make the denominator not equal; hence this limit DNE because the denominator is zero.

Consider the domain of the function. Because this equation is a polynomial, n is not restricted by any value. Thus the way to evaluate this limit would simply be to plug the value that n is approaching into the limit equation.

Consider the domain of the function. Because this equation is a polynomial, x is not restricted by any value. Thus the way to evaluate this limit would simply be to plug the value that x is approaching into the limit equation.

The limiting situation in this equation would be the denominator. Plug the value that n is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will equal zero when n=4; so we try to eliminate the denominator by factoring. When the denominator is no longer zero, we may continue to insert the value of n into the remaining equation.

The limiting situation in this equation would be the denominator. Plug the value that n is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will equal zero when n=-3; so we try to eliminate the denominator by factoring. When the denominator is no longer zero, we may continue to insert the value of n into the remaining equation.

The limiting situation in this equation would be the denominator. Plug the value that n is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will equal zero when n=-1; so we try to eliminate the denominator by factoring. When the denominator is no longer zero, we may continue to insert the value of n into the remaining equation.

Using the graph provided above, we can observe the behavior of the function as  from the left to determine that 

Using the graph provided above, we can observe the behavior of the function as   to determine that 

Using the graph provided above, we can observe the behavior of the function as   to determine that  does not exist. This is because the one-sided limits as  are different; as  from the left, the limit equals , but as  from the right, the limit equals .