Mohon bantuannya : Limit
a. 5
b. 4
c. 3
d. 0
e. -2
a. 5
b. 4
c. 3
d. 0
e. -2
izharulhaq78
1 votes
Thanks 2
Takamori37
Selama cos(2x) tidak bermasalah, sehingga:
![$\begin{align}\lim_{x\to0}\frac{x^2+\sin^2(2x)}{x^2\cos(2x)}&=\lim_{x\to0}\frac1{\cos(2x)}\times\lim_{x\to0}\frac{x^2+\sin^2(2x)}{x^2} \\ &=\frac{1}{\cos(2(0))}\times\left[\lim_{x\to0}\frac{x^2}{x^2}+\lim_{x\to0}\frac{\sin^2(2x)}{x^2}\right] \\ &=\frac1{\cos0}\times\left[1+\left(\lim_{x\to0}\frac{\sin(2x)}{x}\right)^2\right] \\ &=\frac11\times(1+2^2) \\ &=1\times(1+4) \\ &=5 \ \ [A]\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7D%5Clim_%7Bx%5Cto0%7D%5Cfrac%7Bx%5E2%2B%5Csin%5E2%282x%29%7D%7Bx%5E2%5Ccos%282x%29%7D%26%3D%5Clim_%7Bx%5Cto0%7D%5Cfrac1%7B%5Ccos%282x%29%7D%5Ctimes%5Clim_%7Bx%5Cto0%7D%5Cfrac%7Bx%5E2%2B%5Csin%5E2%282x%29%7D%7Bx%5E2%7D+%5C%5C+%26%3D%5Cfrac%7B1%7D%7B%5Ccos%282%280%29%29%7D%5Ctimes%5Cleft%5B%5Clim_%7Bx%5Cto0%7D%5Cfrac%7Bx%5E2%7D%7Bx%5E2%7D%2B%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%5Csin%5E2%282x%29%7D%7Bx%5E2%7D%5Cright%5D+%5C%5C+%26%3D%5Cfrac1%7B%5Ccos0%7D%5Ctimes%5Cleft%5B1%2B%5Cleft%28%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%5Csin%282x%29%7D%7Bx%7D%5Cright%29%5E2%5Cright%5D+%5C%5C+%26%3D%5Cfrac11%5Ctimes%281%2B2%5E2%29+%5C%5C+%26%3D1%5Ctimes%281%2B4%29+%5C%5C+%26%3D5+%5C+%5C+%5BA%5D%5Cend%7Balign%7D "$\begin{align}\lim_{x\to0}\frac{x^2+\sin^2(2x)}{x^2\cos(2x)}&=\lim_{x\to0}\frac1{\cos(2x)}\times\lim_{x\to0}\frac{x^2+\sin^2(2x)}{x^2} \\ &=\frac{1}{\cos(2(0))}\times\left[\lim_{x\to0}\frac{x^2}{x^2}+\lim_{x\to0}\frac{\sin^2(2x)}{x^2}\right] \\ &=\frac1{\cos0}\times\left[1+\left(\lim_{x\to0}\frac{\sin(2x)}{x}\right)^2\right] \\ &=\frac11\times(1+2^2) \\ &=1\times(1+4) \\ &=5 \ \ [A]\end{align}")
1 votes
Thanks 1
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