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Questions on limits and L'Hôpital's Rule?
I'm taking the derivative, but can't seem to get the right solution (comparing to answers in back of book). Can someone help me out and show me how to solve these?
Determine whether the limits exist, and where possible evaluate it.
1) lim as x-->1 of lnx/x^2-1
2) lim as x-->0 of sinh(2x)/x
3) lim as t-->pi of sin^2t/t-pi
4) lim as x-->0 of 1-cosh(3x)/x
I would greatly appreciate help on how to answer these. Thanks so much!
1 Answer
- 1 decade agoFavorite Answer
First, plug in the limit value... looking at problem #1, plug in the value 1 for x. ln 1 = 0 and 1-1 = 0 ... therefore we can use L'Hopital's (since the top and bottom numbers are equal).
When using L'Hopitals, simply take the derivative of the top and bottom, and again, plug in the x value.
deirvative of ln x = 1/x
derivative of x^2 - 1 = 2x
so we have (1/x) / 2x which equals 1 / 2x^2..... now plug in x=1 and you get 1/2. The limit to #1 should be 1/2.
And repeat the pattern for the rest!!!
