quiz6-sol

# quiz6-sol - AMS 151(Fall 2009 Joe Mitchell Applied Calculus...

This preview shows pages 1–2. Sign up to view the full content.

AMS 151 (Fall, 2009) Joe Mitchell Applied Calculus I Quiz # 6 – Solution Notes 1. (4 points) Compute lim t + 12 te 1 /t - 12 t . We rewrite the expression: lim t + 12 te 1 /t - 12 t = lim t + 12( e 1 /t - 1) 1 /t , and then see that it is of the form 0 0 , so we apply l’Hopital’s rule to get lim t + 12( e 1 /t - 1) 1 /t = lim t + 12( e 1 /t ( - 1 /t 2 )) - 1 /t 2 = lim t + 12 e 1 /t = 12 . 2. (4 points) Compute lim t 0 + 1 t - 1 e t 1 . We rewrite the expression by writing with a common denominator: lim t 0 + 1 t - 1 e t - 1 = lim t 0 + e t - 1 - t t ( e t - 1) , and then see that it is of the form 0 0 , so we apply l’Hopital’s rule to get lim t 0 + e t - 1 - t t ( e t - 1) = lim t 0 + e t - 1 te t + e t - 1 , and see that it is still of the form 0 0 , so we apply l’Hopital’s rule again to get lim t 0 + e t - 1 te t + e t - 1 = lim t 0 + e t te t + e t + e t = 1 2 . 3. (4 points)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

quiz6-sol - AMS 151(Fall 2009 Joe Mitchell Applied Calculus...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online