Question

1)lim x^2
x->4
2)lim x^2-1//2x^2-x-1
x->1
3)lim x^2-1//2x^2-x-1
x->бесконечности
4)lim x^2-1//2x^2-x-1
x->0
5)lim x^3-1//x^2-1
x^2-1
6)lim sin x4//2x
x->0

Answer 1

$lim_{x to 4} x^{2} = 4^{2} =16 \ lim_{x to1} frac{ x^{2} -1}{2 x^{2} -x-1} = frac{ 1 ^{2} -1}{2 *1^{2} -1-1} = frac{0}{0} = textgreater lim_{x to1} frac{ x^{2} -1}{2 x^{2} -x-1}= frac{(x-1)(x+1)}{(x-1)2x+1}$$=frac{x+1}{2x+1} = =frac{1+1}{2*1+1} = frac{2}{3} \ lim_{x to infty} frac{ x^{2} -1}{2 x^{2} -x-1} = frac{infty}{infty} = textgreater lim_{x to infty} frac{ x^{2} -1}{2 x^{2} -x-1}= frac{1}{2} \ lim_{x to 0} frac{ x^{2} -1}{2 x^{2} -x-1}= frac{ -1}{-1}=1 \ 6) lim_{x to0} sin frac{x ^{4} }{2x} =sin frac{ x^{3} }{2} =0$