# How do you solve #lim _ { x \rightarrow - 1} \frac { 2x ^ { 3} + 5x ^ { 2} + 4x + 1} { 3x ^ { 3} + 5x ^ { 2} + x - 1}#?

See below.

The numerator and denominator are both polynomials.

Factor by trial and error or by polynomial division, reduce the fraction, and try again to find the limit.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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