Question

Help with Limits... See diagram and I need an explination please

Answer 1

\[\lim_{h \rightarrow 0} \frac{ \cos(\frac{ \pi }{ 2 } +h) }{ h}\] is what?
A) 1
B) nonexistent
C) 0
D) -1
E) none of these

Answer 2

Hmm there's probably some identity I'm forgetting for this one...

But it does appear that we're getting the form 0/0.
So we can always turn to good ole L'Hopital in that case.

Have you learned `L'Hopital's Rule` ?

Answer 3

No I have not. What is it?

Answer 4

If you haven't, then let's not cheat XD haha.
It's a fun little shortcut.. but I guess we're supposed to use some type of identity for this one hmm.

Answer 5

haha. darn. Well I am in Calc BC; Im bound to learn it soon. And yeah this type of question has always stumpped me since Calc AB. I have no idea what to do.

Answer 6

\[\cos (\alpha+\beta)=\cos \alpha \cos \beta-\sin \alpha \sin \beta\] from this\[\cos \left( \frac{ \pi }{ 2 }+h \right)=-\sin h\] now\[\lim_{h \rightarrow 0}\ \frac{ \cos (\frac{ \pi }{ 2 }+h) }{ h }=\lim_{h \rightarrow 0}\frac{ -\sin h }{ h }=-\lim_{h \rightarrow 0}\frac{ \sin h }{ h }=-1\]

Answer 7

yes theanswer is -1 le0n solution is right

Answer 8

If you are in BC calc you WILL learn this eventually.