Evaluate the following limits, or state that they do not exist. Use - infinity a

Question

Evaluate the following limits, or state that they do not exist. Use - infinity and infinity when appropriate. lim_x rightarrow 5^+ -2/(x - 5)^2 lim_x rightarrow 5^- -2/(x - 5)^2 lim_x rightarrow 5 - 2/(x - 5)^2 Select the correct choice below, and fill in the answer box if necessary. lim_x rightarrow 5^- -2/(x - 5)^2 = (Simplify your answer.) The limit does not exist. Select the correct choice below, and fill in the answer box if necessary. lim_x rightarrow 5 -2/(x - 5)^2 = (Simplify your answer.) The limit does not exist.

Explanation / Answer

a) When x is tending to 5+ the denominator will be the square of a very small number thus nemrator will become very large (infinite) but with a negative sign so limit is = -infinite

b) The same holds true for x tending to 5- ; since it is to be squared the sign doesn't matter and teh value will come out to be - infinity;

c) since both value of limit tending to 5+ and 5- are the same, the limit at x tending to 5 will exist and will be equal to both the limits which is = - infinite

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