Question

Trig limits:

Answer 1

http://prntscr.com/2w2p3l

Answer 2

As you see its a 0/0 type limit. An indeterminate form, so use the L'hospital's rule!

Answer 3

We can't use L'hospital's rule.

Answer 4

Why's that?

Answer 5

It's a beginning calculus course, we're not suppose to know that rule yet xD

Answer 6

u can do it this way...
\[\lim_{x \rightarrow \pi/4} \frac{ 3 ( 1 - tanx) }{ sinx - cosx }\]\[\lim_{x \rightarrow \pi/4}\frac{ 3( 1- \frac{ sinx }{ cosx }) }{ sinx - \cos x }\]\[\lim_{x \rightarrow \pi/4}\frac{ -3(sinx - \cos x) }{ cosx( sinx - \cos x) }\]\[- \lim_{x \rightarrow \pi/4} \frac{ 3 }{ cosx }\]\[-3 \lim_{x \rightarrow \pi/4}\frac{ 1 }{ \cos x }\]\[= -3 \sqrt{2}\]

Answer 7

Yup, thank you :)

Answer 8

u r welcome !

Answer 9

By algebraic simplification. You will learn that rule later in the future.