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1.![lim_{x to 2} frac{sqrt{x+2}-2}{x^{2}-4}= lim_{x to 2} frac{x-2}{(x^{2}-4)(sqrt{x+2}+2)}= lim_{x to 2} frac{sqrt{x+2}-2}{x^{2}-4}= lim_{x to 2} frac{x-2}{(x^{2}-4)(sqrt{x+2}+2)}=](https://tex.z-dn.net/?f=+lim_%7Bx+to+2%7D+frac%7Bsqrt%7Bx%2B2%7D-2%7D%7Bx%5E%7B2%7D-4%7D%3D+lim_%7Bx+to+2%7D+frac%7Bx-2%7D%7B%28x%5E%7B2%7D-4%29%28sqrt%7Bx%2B2%7D%2B2%29%7D%3D)
![lim_{x to 2} frac{1}{(x+2)(sqrt{x+2}+2)}= frac{1}{(2+2)(2+2)} = frac{1}{16} lim_{x to 2} frac{1}{(x+2)(sqrt{x+2}+2)}= frac{1}{(2+2)(2+2)} = frac{1}{16}](https://tex.z-dn.net/?f=lim_%7Bx+to+2%7D+frac%7B1%7D%7B%28x%2B2%29%28sqrt%7Bx%2B2%7D%2B2%29%7D%3D+frac%7B1%7D%7B%282%2B2%29%282%2B2%29%7D+%3D+frac%7B1%7D%7B16%7D+)
2.![lim_{x to0} frac{1-cos4x}{x^{2}}= lim_{x to0}frac{2sin^{2}2x}{x^{2}}= lim_{x to0} frac{1-cos4x}{x^{2}}= lim_{x to0}frac{2sin^{2}2x}{x^{2}}=](https://tex.z-dn.net/?f=+lim_%7Bx+to0%7D+frac%7B1-cos4x%7D%7Bx%5E%7B2%7D%7D%3D+lim_%7Bx+to0%7Dfrac%7B2sin%5E%7B2%7D2x%7D%7Bx%5E%7B2%7D%7D%3D)
![lim_{x to0}2*4*frac{sin2x*sin2x}{2x*2x}=8*1=8 lim_{x to0}2*4*frac{sin2x*sin2x}{2x*2x}=8*1=8](https://tex.z-dn.net/?f=+lim_%7Bx+to0%7D2%2A4%2Afrac%7Bsin2x%2Asin2x%7D%7B2x%2A2x%7D%3D8%2A1%3D8)
3.![lim_{x to infty} (frac{3x-4}{3x-2})^{6x+1}=lim_{x to infty} (1+frac{-2}{3x-2})^{6x+1}= lim_{x to infty} (frac{3x-4}{3x-2})^{6x+1}=lim_{x to infty} (1+frac{-2}{3x-2})^{6x+1}=](https://tex.z-dn.net/?f=+lim_%7Bx+to+infty%7D++%28frac%7B3x-4%7D%7B3x-2%7D%29%5E%7B6x%2B1%7D%3Dlim_%7Bx+to+infty%7D++%281%2Bfrac%7B-2%7D%7B3x-2%7D%29%5E%7B6x%2B1%7D%3D)
![lim_{x to infty} (1+frac{-2}{3x-2})^{ frac{3x-2}{-2}frac{-2}{3x-2} 6x+1}= lim_{x to infty} (1+frac{-2}{3x-2})^{ frac{3x-2}{-2}frac{-2}{3x-2} 6x+1}=](https://tex.z-dn.net/?f=lim_%7Bx+to+infty%7D+%281%2Bfrac%7B-2%7D%7B3x-2%7D%29%5E%7B+frac%7B3x-2%7D%7B-2%7Dfrac%7B-2%7D%7B3x-2%7D+6x%2B1%7D%3D)
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