Posted by Alex on Saturday, February 21, 2009 at 4:39pm.
This question is related to limits.
If you do that, you will get 0/0. You have to take the ratio of the derivatives.
= lim(x->pi/4)(cosx+sinx)/-2 sin(2x)
= sqrt 2/(-2) = -0.707
That's called using L'Hopital's rule for indeterminate-ratio limits. It works for 0/0 or infinity/infinity. Try it with a number close to pi/4, such as 0.785, and you will see that it gives the right answer.
if you put in PI/4 in to the x, you will get an indeterminate form 0/0.
Lim (sinx/cos2x - cosx/cos2x)
multiply numerator and denominator by (sinx+cosx)
lim (sin^2x -cos^2x)/cos2x(sinx+cosx)
lim 1/(sinx+cosx)= 1/sqrt2
looking at drwls answer, using L'Hopitals rule (I assumed you had not gotten to it yet), I see I must have made a sign error, you can find it.
Thanks. Actually i did not learn that other rule yet and I don't think we will but thanks anyway it was helpful.
I solved using bobpursley's idea and got sqrt2/2=1/sqrt2.
I have a similar question relating to limits that I solved
I multiplied the numerator and denominator by (1+cosx) to get
the lim(x->0) (sinx/x)^2 would =1
I then substituted the remaining portion with 0 and got 1/4
Is this answer right??
Calculus..more help! - I have a question relating to limits that I solved lim(x...
calculus - calculate the lim as x-> pi (cos(x)+1)/(x-pi) using the ...
math - i need some serious help with limits in pre-calc. here are a few ...
calculus - The limit represents the derivative of some function f at some number...
Calculus - Below are the 5 problems which I had trouble in. I can't seem to ...
Calculus - Find the following limits algebraically or explain why they don...
Calculus - Using L'Hopital's rule find the limit if exists of; lim x-&...
Calculus - Evaluate the following limit: lim x->(pi/2) [((pi/2)-(x))/cosx...
Maths Calculus Derivatives & Limits - Using the definition of the ...
calc - need to find: lim as x -> 0 of 4(e^2x - 1) / (e^x -1) Try ...
For Further Reading