Chapter 4 | Applications of Derivatives
471
xe 1/ x
lim x →∞
391.
x 1/cos x
lim x →0 +
392.
x 1/ x
lim x →0 +
393.
x
⎛ ⎝ 1− 1 x
⎞ ⎠
lim x →0 -
394.
x
⎛ ⎝ 1− 1 x
⎞ ⎠
lim x
395.
→∞
For the following exercises, use a calculator to graph the function and estimate the value of the limit, then use L’Hôpital’s rule to find the limit directly.
e x −1 x
396. [T] lim x →0
⎛ ⎝ 1 x
⎞ ⎠
397. [T] lim x →0
x sin
x −1 1−cos( πx ) e ( x −1) −1 x −1
398. [T] lim x →1
399. [T] lim x →1
( x −1) 2 ln x 1+cos x sin x
400. [T] lim x →1
401. [T] lim x → π
402. [T] lim x →0 ⎛ 403. [T] lim x →0 +
⎝ csc x − 1 x ⎞ ⎠
tan( x x )
ln x sin x
404. [T] lim x →0 +
e x − e − x x
405. [T] lim x →0
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