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# Evaluate the limit. if the limit does not exist explain why. a) lim[x:(-2),(x^3+8)/(x+2)]?

b) lim[x:5,(x-5)/|x-5|]

c)lim[x:8,1/(x-8)]

it would help a lot if you guy can show the work so i can learn how to do it! thank

### 4 Answers

- 7 years agoFavorite Answer
for problems of the type 0/0 or inf/inf, one uses a concept call L'Hopital's rule in order to simplify the equation. Look it up on wikipedia

a) with x : -2, the equation reduces to the form 0/0. Hence you can use L'Hopital's rule.

Differentiating numerator and denominator, w.r.t. x

required limit = lim [x:-2], 3x^2 = 3(-2)^2 = 12

b) this is again of the form 0/0, so differentiate w.r.t x, which means required limit = 1

c) this one is of the form 1/0 so you cannot use the rule. The limit in this case is "infinity"

Source(s): Graduate in Applied Physics - 4 years ago
factor the denominator (x^3+8) utilising sum of ideal cubes and then component to it is going to cancel with the numerator (x+2). Then stick in -2 everywhere you spot an x and notice what it provides. this could be your answer.