# Limit help (two problems)

• Sep 19th 2011, 01:36 PM
riddikulus
Limit help (two problems)
I have been trying to figure out these limit problems and I get stuck on trying to move the function around to make it possible to solve.

The first one is:

lim sinx - cosx / tanx - 1
x--> (pi/4)

All I've gotten so far is to replace tanx with sinx/cosx but I don't even know if that's the way to go...

the second is:

lim sqrt(a + 2h) - sqrt(a) / h
h-->0

I tried multiplying by the conjugate, but when I multiply things out, I get stuck at:

2h / h*sqrt(a+2h) + sqrt(a)

pleaseeee help me. I have no idea how to move on from here; I'm terrible at figuring out what to do next in these situations.
• Sep 19th 2011, 01:48 PM
Plato
Re: Limit help (two problems)
Quote:

Originally Posted by riddikulus
The first one is:
lim sinx - cosx / tanx - 1
x--> (pi/4)

$\displaystyle \frac{\sin(x)-\cos(x)}{\tan(x)-1}=\frac{\cos(x)[\sin(x)-\cos(x)]}{\sin(x)-\cos(x)}$
• Sep 19th 2011, 02:11 PM
riddikulus
Re: Limit help (two problems)
where did you get that though?
• Sep 19th 2011, 02:14 PM
Plato
Re: Limit help (two problems)
Quote:

Originally Posted by riddikulus
where did you get that though?

Multiply numerator and denominator by $\displaystyle \cos(x).$
• Sep 19th 2011, 02:22 PM
riddikulus
Re: Limit help (two problems)
okay but then you still get zero on the bottom, so what do you do next? i seriously have no idea how to shift trig fxns or anything, for that matter.
• Sep 19th 2011, 02:25 PM
Plato
Re: Limit help (two problems)
Quote:

Originally Posted by riddikulus
okay but then you still get zero on the bottom, so what do you do next? i seriously have no idea how to shift trig fxns or anything, for that matter.

Can you do basic algebra?
Divide out $\displaystyle \sin(x)-\cos(x)$