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How do you evaluate the limit #(2p+4)/(3p)# as p approaches #-2#?

Answer 1

Christopher Allers

Essentially, by Subsitution.

As #p# approaches #-2# the denominator does not go to #0#, so we can simply say:

As #p rarr-2 =>2p+4 rarr 2(-2) + 4 = 0# and #3p rarr -6#, so

#(2p+4)/(3p) rarr 0/(-6) = 0#

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Answer 2

Elijah Abram

To evaluate the limit (2p+4)/(3p) as p approaches -2, substitute -2 for p in the expression and simplify.

(2(-2)+4)/(3(-2)) = (0)/(-6) = 0/6 = 0

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Answer 3

Christopher Allers

To evaluate the limit (\lim_{p \to -2} \frac{2p+4}{3p}), we can substitute -2 for p in the expression (\frac{2p+4}{3p}) and simplify:

[ \lim_{p \to -2} \frac{2p+4}{3p} = \frac{2(-2)+4}{3(-2)} = \frac{-4+4}{-6} = \frac{0}{-6} = 0 ]

So, the limit is 0.

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Answer from HIX Tutor

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.