limits/trig

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krokal

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Sep 8, 2005
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Can someone help me with these problems?

1) Limit of (t^2-1)/sin(t-1) as t approaches 0

I know the answer is 1, but I don't know how to get there. I expanded the numerator to (t-1)(t+1), but I don't think it is possible to reduce the (t-1)'s...

2) Limit of 2x/tan3x as x approaches 0

The answer is 2/3,but I don't know how to do this one either.

3) Limit of ((x-(pi/4))^2)/(tan(x-1))^2 as x approaches pi/4
 
I don't know if the first or last one are typed in right or not, but it seems to me how they are written you can find the limit directly. #2 is different though. You'll have to use L'Hopital's rule. Take the derivative of the top and the derivative of the bottom (not quotent rule) and set those as a ratio and see if the limit exists. You can keep doing it until you get a limit.

For example...the limit of

x/(x^2-1) as x approaches -1.

Der of x = 1
Der of (x^2 - 1) = 2x
1/(2x) as x approaches -1 = -0.5
 
this help?
Code: 
#1

                   t^2-1
lim t->0       -----------
                   sin(t-1)

#3

                     (   x-   pi       ) ^2
                     (        ---       )
                     (         4        )
lim x->pi/4          -------------------
                       (tan x-1)^2
 
No. Just plug in 0 for t.

I get -1/sin(-1) for #1

#3
Just plug in pi/4 for t.
I get 0. 0/(tan(-3pi/4))^2 = 0
 
How do I do 1 and 3 without plugging in #'s? Isn't there a way to do it algebraically?
 
You need to reread what a limit is. At some point you HAVE TO plug in #s. That is how you determine what the limit is if one exists. You can graph the function and see what y value the graph is approaching at the x value in question. But as far as I know, that's the only way to find the limit.
 
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