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.

Re: Limit help (two problems)

Quote:

Originally Posted by

**riddikulus** The first one is:

lim sinx - cosx / tanx - 1

x--> (pi/4)

$\displaystyle \frac{\sin(x)-\cos(x)}{\tan(x)-1}=\frac{\cos(x)[\sin(x)-\cos(x)]}{\sin(x)-\cos(x)}$

Re: Limit help (two problems)

where did you get that though?

Re: Limit help (two problems)

Quote:

Originally Posted by

**riddikulus** where did you get that though?

Multiply numerator and denominator by $\displaystyle \cos(x).$

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.

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 $\displaystyle \sin(x)-\cos(x)$