Question

Lim 5/3x^3-5x
x-> бесконечность
Lim 2x^2-1/4-7x^2
x->бесконечность
Lim x^2-16/корень x-2
x->4
Lim Sin3x-Sin x/x
x->0

Answer 1

$1) lim_{x to infty} frac{5}{3x ^{2}-5x }=( frac{5}{infty})=0 \2) lim_{x to infty} frac{2 x^{2} -1}{4-7 x^{2} } =( frac{infty}{infty}) = lim_{x to infty} frac{frac{2 x^{2}}{ x^{2} } -frac{1}{ x^{2} }}{frac{4}{ x^{2} }-frac{7 x^{2}}{ x^{2} } }= frac{2-0}{0-7}=- frac{2}{7}$
$3) lim_{x to 0} frac{sin3x-sinx}{x} =lim_{x to 0} frac{2sin frac{3x-x}{2}cdot cos frac{3x+x}{2} }{x}= \ =lim_{x to 0} frac{2sinx }{x} cdot lim_{x to 0} cos frac{3x+x}{2} =2cdot1=2$