1. Find the indicated limit. (Be careful, L’Hospital’s Rule does not always apply and when it does, it is not always helpful.)
 

a. 

ANS: Because the numerator is tending to 28 and the denominator is tending to 7, L’Hospital’s Rule does not apply. The answer is simply 28/7

b. 

ANS: Applying L’Hospital’s Rule we have

c. 

ANS: Applying L’Hospital’s Rule (twice) we have

d. 

ANS: Since the numerator tends to 1 and the denominator tends to zero, L’Hospital’s Rule does not apply. Since the denominator is always positive and the numerator is positive as long as x is near 0, the limit is + infinity.

e. 

ANS: This can be done without L’Hospital’s Rule, since an x may be canceled out of both the numerator and denominator. The limit is 1/3.

f. 

ANS: Although L’Hospital’s Rule applies to this limit, it does not help you (as you will see after one application).

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2. Write the quantity  as one fraction and use this to find .

ANS: Simplifying the expression and then applying L’Hospital’s Rule (three times), we have

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