2nd question: Find lim (sin2xcot4x) X->0.

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2nd question: Find lim (sin2xcot4x) X->0.

Mathematics
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are you allowed to use l'hopital's rule?
assuming this is \[\lim_{x\rightarrow 0}\sin(2x)\cot(4x)\] \[\lim_{x\rightarrow 0}\frac{\sin(2x)\cos(4x)}{\sin(4x)}\]
1/2

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in any case the answer is \[\frac{1}{2}\]
but if you need to show your work your answer will depend on what you are allowed to use. l'hopital's rule is the simplest, otherwise it will be some work
i dont know the hospital rule that you have said :(
you mean you do not know it or you are not allowed to use it? i assume this is calc class, so hve you covered deriviatives yet or are you just starting out?
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without using l'hopital rule
any computation as a long the answer will be the same in a long method
i dont know it sorry :(
there is a nice neat answer above. i think you can also use \[\frac{sin(2x)\cos(4x)}{\sin(4x)}=\frac{\sin(2x)(\cos^2(2x)-\sin^2(2x))}{2\sin(2x)\cos(2x)}\]
here i used the double angle formula for sine and cosine
can i post the 3rd question too?
then cancel the sin(2x) top and bottom, get \[\frac{\cos^2(2x)-\sin^2(2x)}{2\cos(2x)}\] replace x by zero, get \[\frac{1}{2}\]
no limit to the amount you can post
yes i will write your solution :)
if f(x)=tanx-x and g(x)=x^3, evaluate the limit of f(x) over g(x) as x approaches 0. -3rd question.
@nenadmatematica if you can do this without l'hopital or power series i will be impressed
haha I just wanted to ask you the same thing :D ....
lol well, i guess we cannot give an elementary reason for this. the answer is \[\frac{1}{3}\] but i cannot think of a gimmick to simplify this expression. are you sure you have not covered l'hopital? because i am stumped. in particular you have a trig fuction combined in combination with x and x^3 so there is no simple trig identity that will change the form of this for you
@nenadmatematika tahnks for helping us too :)
well you're welcome....I agree with satellite that this example is very convenient for using L'Hopital rule.....I can't think of any other way now :D
i really dont know but if both of you wants to use L'hopital rule. then i will agree to both of you
4th question: Evaluate the lim x^2-16 over x+4 as x->4.

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