I just spent almost 40 minutes on a single calculus exam problem. It was the last question too.
lim x->0 ( (3x^2 - 1) * cos^2(x) + 1 ) / ( 3x^2) )
I was able to plug in that cos^2(x) = 1 - sin^2(x). After that I had no fucking clue.
Calc-bros of /sci/, tell me how much of an idiot I am?
>mfw I don't understand any of this shit as I'm still learning quadratics
[eqn] 3x^2 \cos ^2 (x) - \cos ^2 (x) + 1 = 3x^2 (1- \sin ^2 (x) ) - 1 +sin ^2(x) +1 = 3x^2 (1- \sin ^2 (x) ) +sin ^2(x) = 3x^2 - 3x^2 \sin ^2 (x) + \sin ^2 (x) = 3x^2 (1- 2 \sin ^2 (x) ) [/eqn] Cancel numerator and denominator. Limit is 1