Question

!!!!!!!!!!!!Предел функции! за решение 30 пунктов!!!!!!!!!!!!!!

Answer 1

$1) lim_{x to infty} frac{3+x+5x^4}{x^4-12x+1}=[frac{infty}{infty}]= lim_{x to infty} frac{5x^4}{x^4}=5 \ \ \ 2) lim_{x to 0} frac{sqrt{1+3x}-sqrt{1-3x}}{x+x^2}= \ \ = lim_{x to 0} frac{(sqrt{1+3x}-sqrt{1-3x})(sqrt{1+3x}+sqrt{1-3x})}{(x+x^2)(sqrt{1+3x}+sqrt{1-3x})}= \ \ =lim_{x to 0} frac{1+3x-1+3x}{x(1+x)(sqrt{1+3x}+sqrt{1-3x})}= \ \ =lim_{x to 0} frac{6}{(1+x)(sqrt{1+3x}+sqrt{1-3x})}=frac{6}{(1+0)(1+1)}=frac{6}{2}=3$

 

$3) lim_{x to pi/4} frac{cos^2x}{sin^3x}=frac{cos^2(pi/4)}{sin^3(pi/4)}=(frac{sqrt2}{2})^2 :(frac{sqrt2}{2})^3=frac{2}{4}*frac{8}{2sqrt2}= \ \ =frac{2}{sqrt2}=frac{2sqrt2}{sqrt2*sqrt2}=frac{2sqrt2}{2}=sqrt2$

Answer 2

мой вариант решения во вложении