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По правилу Лопиталя
1)![lim x->oo frac{5x^3+3x^5-5sqrt{x}+1}{4x^3+2x^5-7}\
lim x->oo frac{15x^2+15x^4-frac{5}{2sqrt{x}}}{12x^2+10x^4}\
lim x->oo frac{30x+60x^3+frac{5}{4sqrt[3]{x}}}{24x+40x^3}\
lim x->oo frac{30+180x^2-frac{15}{8sqrt[5]{x}}}{24+120x^2}=oo lim x->oo frac{5x^3+3x^5-5sqrt{x}+1}{4x^3+2x^5-7}\
lim x->oo frac{15x^2+15x^4-frac{5}{2sqrt{x}}}{12x^2+10x^4}\
lim x->oo frac{30x+60x^3+frac{5}{4sqrt[3]{x}}}{24x+40x^3}\
lim x->oo frac{30+180x^2-frac{15}{8sqrt[5]{x}}}{24+120x^2}=oo](https://tex.z-dn.net/?f=lim+x-%26gt%3Boo++frac%7B5x%5E3%2B3x%5E5-5sqrt%7Bx%7D%2B1%7D%7B4x%5E3%2B2x%5E5-7%7D%5C%0Alim+x-%26gt%3Boo++frac%7B15x%5E2%2B15x%5E4-frac%7B5%7D%7B2sqrt%7Bx%7D%7D%7D%7B12x%5E2%2B10x%5E4%7D%5C%0Alim+x-%26gt%3Boo++frac%7B30x%2B60x%5E3%2Bfrac%7B5%7D%7B4sqrt%5B3%5D%7Bx%7D%7D%7D%7B24x%2B40x%5E3%7D%5C%0Alim+x-%26gt%3Boo++frac%7B30%2B180x%5E2-frac%7B15%7D%7B8sqrt%5B5%5D%7Bx%7D%7D%7D%7B24%2B120x%5E2%7D%3Doo)
2)Опять
![lim x->4 frac{3x^2-5x-28}{x^3-64}\
lim x->4 frac{6x-5}{3x^2}=frac{19}{48} lim x->4 frac{3x^2-5x-28}{x^3-64}\
lim x->4 frac{6x-5}{3x^2}=frac{19}{48}](https://tex.z-dn.net/?f=lim+x-%26gt%3B4+++frac%7B3x%5E2-5x-28%7D%7Bx%5E3-64%7D%5C%0Alim+x-%26gt%3B4+++frac%7B6x-5%7D%7B3x%5E2%7D%3Dfrac%7B19%7D%7B48%7D)
3)Опять
![lim x->2 frac{arctg(sqrt{6-x}-2)}{x^2-4}\
lim x->2 frac{frac{1}{2sqrt{6-x}(x+4sqrt{6-x}+11)}}{2x}=-frac{1}{16}\
lim x->2 frac{arctg(sqrt{6-x}-2)}{x^2-4}\
lim x->2 frac{frac{1}{2sqrt{6-x}(x+4sqrt{6-x}+11)}}{2x}=-frac{1}{16}\](https://tex.z-dn.net/?f=lim+x-%26gt%3B2+frac%7Barctg%28sqrt%7B6-x%7D-2%29%7D%7Bx%5E2-4%7D%5C%0Alim+x-%26gt%3B2+frac%7Bfrac%7B1%7D%7B2sqrt%7B6-x%7D%28x%2B4sqrt%7B6-x%7D%2B11%29%7D%7D%7B2x%7D%3D-frac%7B1%7D%7B16%7D%5C%0A)
4)![limx->5 frac{x^2-7x+10}{sqrt{2x-1}-sqrt{4+x}}\
limx->5 frac{2x-7}{ frac{2sqrt{x-4}-sqrt{2x-1}}{2sqrt{(x+4)(2x-1)}}}=18 limx->5 frac{x^2-7x+10}{sqrt{2x-1}-sqrt{4+x}}\
limx->5 frac{2x-7}{ frac{2sqrt{x-4}-sqrt{2x-1}}{2sqrt{(x+4)(2x-1)}}}=18](https://tex.z-dn.net/?f=limx-%26gt%3B5+frac%7Bx%5E2-7x%2B10%7D%7Bsqrt%7B2x-1%7D-sqrt%7B4%2Bx%7D%7D%5C%0Alimx-%26gt%3B5+frac%7B2x-7%7D%7B+frac%7B2sqrt%7Bx-4%7D-sqrt%7B2x-1%7D%7D%7B2sqrt%7B%28x%2B4%29%282x-1%29%7D%7D%7D%3D18)
5)
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2)Опять
3)Опять
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