Calc

I'm feeling retarded and need halp:
lim x->0 sin4x/sin6x=?
also
Given y=sin2x-2sinx, find dy/dx=0
also
Given f(x)=xg(x^2), find f'' in terms of g,g',g''
Any help would be much appreciated!

lim x->0 sin4x/sin6x = lim x->0 4cos4x/6cos6x (l'Hopital) = 4*1/6*1 = 2/3
 btw. (f(g))'=g'*f'(g)
y=sin2x-2sinx y'=2cos2x-2cosx

f(x)=xg(x^2) f'(x)=x*2xg'(x^2)+g(x^2)=2x^2*g'(x^2)+g(x^2)
f''(x)=4x*g'(x^2)+2x^2*2x*g''(x^2)+2xg'(x^2)=4x^3g''(x^2)+6xg'(x^2)

2/3

sin(x) approaches x as approaches 0
therefore you can say:
lim(x->0) sin(4x)/sin(6x) =>
lim(x->0) 4x/6x =>
2/3

Why not let the computers do the work?


limit(sin(4*x)/sin(6*x), x=0);
                                      2/3

diff(x*g(x^2), x$2);
                               2         3   (2)      2
                       6 D(g)(x ) x + 4 x  (D   )(g)(x )

Whoops, I forgot the second.

_EnvAllSolutions := true:
solve(diff(sin(2*x)-2*sin(x), x) = 0);
                  2 Pi _Z1~, 2/3 Pi - 4/3 Pi _B1~ + 2 Pi _Z1~

Where B1~ = {0,1} and _Z1~ is an integer.

>>4
Because then you don't learn anything, except how to program computers.

I've just read this thread and all I got was: asjdhgkucay3737jk huyv787

I feel dazzled and flabbergasted

>>3
You better be joking.  That is incorrect, and either you understand this or you have no place in this thread.