Question

can anyone help me?
http://imgur.com/cb6mcid

Answer 1

Did you use the hint?

Answer 2

yea but for some reason i get stuck :<

Answer 3

Where did you get stuck at?

Answer 4

\[
\lim_{\Delta x\to0}\frac{\sin(\pi/6+\Delta x)-(1/2)}{\Delta x}

\]

Answer 5

i got up to this point http://i.imgur.com/hxmZiWD.jpg

Answer 6

Okay there are two familiar limits you should be noticing...

Answer 7

oops accidently put the equal sign in the 2nd part of the picture

Answer 8

\[
\lim_{h\to 0}\frac{\sin(h)}{h}
\]And \[
\lim_{h\to 0}\frac{\cos(h)-1}{h}

\]

Answer 9

anal

Answer 10

@ineptAtMath Do you see where they're at?

Answer 11

\(\bf \cfrac{1}{2}cos(\Delta x)+\cfrac{\sqrt{3}}{2}sin(\Delta x)-\cfrac{1}{2} \implies \cfrac{cos(\Delta x)+\sqrt{3}sin(\Delta x)-1}{2}\\\quad \\
\cfrac{
\cfrac{1}{2}cos(\Delta x)+\cfrac{\sqrt{3}}{2}sin(\Delta x)-\cfrac{1}{2}
}{
\Delta x
} \implies
\cfrac{
\cfrac{cos(\Delta x)+\sqrt{3}sin(\Delta x)-1}{2}
}{
\Delta x
}\\\quad \\
\cfrac{cos(\Delta x)+\sqrt{3}sin(\Delta x)-1}{2} \times \cfrac{1}{\Delta x} \implies
\cfrac{cos(\Delta x)+\sqrt{3}sin(\Delta x)-1}{2 \Delta x}\\\quad \\
\cfrac{cos(\Delta x)-1}{2\Delta x}+\cfrac{\sqrt{3}sin(\Delta x)}{2\Delta x}\)

Answer 12

\(\bf \cfrac{cos(\Delta x)-1}{2\Delta x}+\cfrac{\sqrt{3}sin(\Delta x)}{2\Delta x} \implies \cfrac{1}{2}\times \cfrac{cos(\Delta x)-1}{\Delta x} + \cfrac{\sqrt{3}}{2}\times \cfrac{sin(\Delta x)}{\Delta x}\)

Answer 13

thanks i managed to get it :D