Friday, 26 April 2013

calculus - How can I solve these trigonometric limits without using L'Hopital's Rule?



Problems with corresponding solutions




I don't understand why #1 is "does not exist" as opposed to 0. I also don't know how to begin solving #2 and #3. When I look it up, the only solutions involve L'Hopital's Rule but my teacher hasn't taught us it yet so I can't use it. Any help is appreciated!


Answer



For the first one the expression under the radical sign is negative for θπ/2 so it is not real.



For the second one multiply top and bottom by 1cosπx and turn the top into sin2πx



Then write the tan2πxof the bottom in terms of sinπx and cosπx and cancel the sin2πx from top and bottom.



The rest is easy.




The third one is similar to the second one.


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...