I'm having difficulty with the algebra/trig portion of this Calculus problem, is it possible to simply it any further? I can't use a calculator or graph to determine the limit, I have to do it with algebra.
lim X->0 [- (4x/(sin2x)) + (x/(cos2x))]
I use the double angle identities to get 2sin(x)cos(x) and cos^2x - sin^2x for the denominators respectively. I can't figure out how to simplify it further, and still get an answer of undefined(which is one of my multiple choices.) Is it possible for me to simplify it further, or is the answer just undefined?
lim X->0 [- (4x/(sin2x)) + (x/(cos2x))]
I use the double angle identities to get 2sin(x)cos(x) and cos^2x - sin^2x for the denominators respectively. I can't figure out how to simplify it further, and still get an answer of undefined(which is one of my multiple choices.) Is it possible for me to simplify it further, or is the answer just undefined?
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lim(x→0) [-4x/sin(2x) + x/cos(2x)]
= lim(x→0) [-2 * 2x/sin(2x) + x/cos(2x)]
= -2 * lim(x→0) 2x/sin(2x) + lim(x→0) x/cos(2x)
= -2 * 1/1 + 0/1, via lim(t→0) sin t/t = 1 with t = 2x
= -2.
I hope this helps!
= lim(x→0) [-2 * 2x/sin(2x) + x/cos(2x)]
= -2 * lim(x→0) 2x/sin(2x) + lim(x→0) x/cos(2x)
= -2 * 1/1 + 0/1, via lim(t→0) sin t/t = 1 with t = 2x
= -2.
I hope this helps!