Nilai lim x mendekati -1 dari x²-1/akar 3x+4 - akar x+2=
Mujee
Jika tidak terbaca lihat lampiran!
![\displaystyle =\lim_{x\to\,-1}\frac{x^2-1}{\sqrt{3x+4}-\sqrt{x+2}}\times\frac{\sqrt{3x+4}+\sqrt{x+2}}{\sqrt{3x+4}+\sqrt{x+2}}\\\\=\lim_{x\to\,-1}\frac{(x-1)(x+1)(\sqrt{3x+4}+\sqrt{x+2})}{3x+4-(x+2)}}\\\\=\lim_{x\to\,-1}\frac{(x-1)(x+1)(\sqrt{3x+4}+\sqrt{x+2})}{2(x+1)}}\\\\=\frac{1}{2}[(-1-1)(\sqrt{-3+4}+\sqrt{-1+2})]\\\\=\frac{1}{2}(-2)(2)\\\\=\boxed{-2}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%3D%5Clim_%7Bx%5Cto%5C%2C-1%7D%5Cfrac%7Bx%5E2-1%7D%7B%5Csqrt%7B3x%2B4%7D-%5Csqrt%7Bx%2B2%7D%7D%5Ctimes%5Cfrac%7B%5Csqrt%7B3x%2B4%7D%2B%5Csqrt%7Bx%2B2%7D%7D%7B%5Csqrt%7B3x%2B4%7D%2B%5Csqrt%7Bx%2B2%7D%7D%5C%5C%5C%5C%3D%5Clim_%7Bx%5Cto%5C%2C-1%7D%5Cfrac%7B%28x-1%29%28x%2B1%29%28%5Csqrt%7B3x%2B4%7D%2B%5Csqrt%7Bx%2B2%7D%29%7D%7B3x%2B4-%28x%2B2%29%7D%7D%5C%5C%5C%5C%3D%5Clim_%7Bx%5Cto%5C%2C-1%7D%5Cfrac%7B%28x-1%29%28x%2B1%29%28%5Csqrt%7B3x%2B4%7D%2B%5Csqrt%7Bx%2B2%7D%29%7D%7B2%28x%2B1%29%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D%5B%28-1-1%29%28%5Csqrt%7B-3%2B4%7D%2B%5Csqrt%7B-1%2B2%7D%29%5D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D%28-2%29%282%29%5C%5C%5C%5C%3D%5Cboxed%7B-2%7D "\displaystyle =\lim_{x\to\,-1}\frac{x^2-1}{\sqrt{3x+4}-\sqrt{x+2}}\times\frac{\sqrt{3x+4}+\sqrt{x+2}}{\sqrt{3x+4}+\sqrt{x+2}}\\\\=\lim_{x\to\,-1}\frac{(x-1)(x+1)(\sqrt{3x+4}+\sqrt{x+2})}{3x+4-(x+2)}}\\\\=\lim_{x\to\,-1}\frac{(x-1)(x+1)(\sqrt{3x+4}+\sqrt{x+2})}{2(x+1)}}\\\\=\frac{1}{2}[(-1-1)(\sqrt{-3+4}+\sqrt{-1+2})]\\\\=\frac{1}{2}(-2)(2)\\\\=\boxed{-2}")
0 votes
Thanks 4
More Questions From This User See All