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26,30
а)
![lim_{x to 1} frac{x^2+2x-3}{x-1} =frac{(x-1)(x+3)}{x-1} =x+3=4 lim_{x to 1} frac{x^2+2x-3}{x-1} =frac{(x-1)(x+3)}{x-1} =x+3=4](https://tex.z-dn.net/?f=+lim_%7Bx+to+1%7D++frac%7Bx%5E2%2B2x-3%7D%7Bx-1%7D+%3Dfrac%7B%28x-1%29%28x%2B3%29%7D%7Bx-1%7D+%3Dx%2B3%3D4)
б)
![lim_{x to -2} frac{x+2}{2x^2+x-6} =frac{x+2}{(x+2)(2x-3)} = frac{1}{2x-3} = -frac{1}{7} lim_{x to -2} frac{x+2}{2x^2+x-6} =frac{x+2}{(x+2)(2x-3)} = frac{1}{2x-3} = -frac{1}{7}](https://tex.z-dn.net/?f=lim_%7Bx+to+-2%7D+frac%7Bx%2B2%7D%7B2x%5E2%2Bx-6%7D+%3Dfrac%7Bx%2B2%7D%7B%28x%2B2%29%282x-3%29%7D+%3D+frac%7B1%7D%7B2x-3%7D+%3D+-frac%7B1%7D%7B7%7D+)
в)
![lim_{x to -1} frac{x+1}{x^2-2x-3} =frac{x+1}{(x-3)(x+1)} = frac{1}{x-3} =- frac{1}{4} lim_{x to -1} frac{x+1}{x^2-2x-3} =frac{x+1}{(x-3)(x+1)} = frac{1}{x-3} =- frac{1}{4}](https://tex.z-dn.net/?f=lim_%7Bx+to+-1%7D+frac%7Bx%2B1%7D%7Bx%5E2-2x-3%7D+%3Dfrac%7Bx%2B1%7D%7B%28x-3%29%28x%2B1%29%7D+%3D+frac%7B1%7D%7Bx-3%7D+%3D-+frac%7B1%7D%7B4%7D+)
г)
![lim_{x to 9} frac{x^2-11x+18}{x-9} = frac{(x-9)(x-2)}{x-9} =x-2=7 lim_{x to 9} frac{x^2-11x+18}{x-9} = frac{(x-9)(x-2)}{x-9} =x-2=7](https://tex.z-dn.net/?f=lim_%7Bx+to+9%7D+frac%7Bx%5E2-11x%2B18%7D%7Bx-9%7D+%3D+frac%7B%28x-9%29%28x-2%29%7D%7Bx-9%7D+%3Dx-2%3D7)
26.31
а)
![lim_{x to -2} frac{x+2}{x^3+8} =frac{x+2}{(x+2)(x^2-2x+4)} = frac{1}{x^2-2x+4} = frac{1}{12} lim_{x to -2} frac{x+2}{x^3+8} =frac{x+2}{(x+2)(x^2-2x+4)} = frac{1}{x^2-2x+4} = frac{1}{12}](https://tex.z-dn.net/?f=lim_%7Bx+to+-2%7D+frac%7Bx%2B2%7D%7Bx%5E3%2B8%7D+%3Dfrac%7Bx%2B2%7D%7B%28x%2B2%29%28x%5E2-2x%2B4%29%7D+%3D+frac%7B1%7D%7Bx%5E2-2x%2B4%7D+%3D+frac%7B1%7D%7B12%7D+)
б)
![lim_{x to -1} frac{1+x^3}{1-x^2} = frac{(x+1)(x^2-x+1)}{(1-x)(1+x)} =frac{(x^2-x+1)}{(1-x)} = frac{3}{2}=1.5 lim_{x to -1} frac{1+x^3}{1-x^2} = frac{(x+1)(x^2-x+1)}{(1-x)(1+x)} =frac{(x^2-x+1)}{(1-x)} = frac{3}{2}=1.5](https://tex.z-dn.net/?f=lim_%7Bx+to+-1%7D+frac%7B1%2Bx%5E3%7D%7B1-x%5E2%7D+%3D+frac%7B%28x%2B1%29%28x%5E2-x%2B1%29%7D%7B%281-x%29%281%2Bx%29%7D+%3Dfrac%7B%28x%5E2-x%2B1%29%7D%7B%281-x%29%7D+%3D+frac%7B3%7D%7B2%7D%3D1.5+)
в)
![lim_{x to 3} frac{x-3}{x^3-27} =frac{x-3}{(x-3)(x^2+3x+9)} =frac{1}{(x^2+3x+9)} = frac{1}{27} lim_{x to 3} frac{x-3}{x^3-27} =frac{x-3}{(x-3)(x^2+3x+9)} =frac{1}{(x^2+3x+9)} = frac{1}{27}](https://tex.z-dn.net/?f=lim_%7Bx+to+3%7D+frac%7Bx-3%7D%7Bx%5E3-27%7D+%3Dfrac%7Bx-3%7D%7B%28x-3%29%28x%5E2%2B3x%2B9%29%7D+%3Dfrac%7B1%7D%7B%28x%5E2%2B3x%2B9%29%7D+%3D+frac%7B1%7D%7B27%7D+)
г)
![lim_{x to 4} frac{16-x^2}{64-x^3} = frac{(4-x)(4+x)}{(4-x)(x^2+4x+16)} = frac{(4+x)}{(x^2+4x+16)} = frac{8}{48} = frac{1}{6} lim_{x to 4} frac{16-x^2}{64-x^3} = frac{(4-x)(4+x)}{(4-x)(x^2+4x+16)} = frac{(4+x)}{(x^2+4x+16)} = frac{8}{48} = frac{1}{6}](https://tex.z-dn.net/?f=lim_%7Bx+to+4%7D+frac%7B16-x%5E2%7D%7B64-x%5E3%7D+%3D+frac%7B%284-x%29%284%2Bx%29%7D%7B%284-x%29%28x%5E2%2B4x%2B16%29%7D+%3D+frac%7B%284%2Bx%29%7D%7B%28x%5E2%2B4x%2B16%29%7D+%3D+frac%7B8%7D%7B48%7D+%3D+frac%7B1%7D%7B6%7D+)
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