Question

найти предел функции

Answer 1

$displaystyle lim_{x to 3} frac{x^2+x-12}{ sqrt{3+x} - sqrt{2x} } =lim_{x to 3} frac{(x+4)(x-3)( sqrt{3+x}+ sqrt{2x} ) }{3-x}=\ \ \ =lim_{x to 3}-(x+4)( sqrt{3+x} + sqrt{2x} )=-14 sqrt{6}$

$displaystyle lim_{x to 0}frac{1-cos 4x}{sin^27x} = lim_{x to 0} frac{2sin^22x}{sin^27x}= lim_{x to 0}frac{2cdot (2x)^2}{(7x)^2} = frac{8}{49}$

$displaystyle lim_{x to infty}bigg( frac{7x+3}{7x+5}bigg)^{7x+4}=lim_{x to infty}bigg(1- frac{2}{7x+5}bigg)^big{ frac{7x+5}{2} - frac{1}{2} } =e^big{- frac{1}{2} }$