Question

очень надо!!Вычислить пределы,помогите,

Answer 1

$1) ...= lim_{x to 5} frac{( sqrt{x-1}-2)( sqrt{x-1}+2)sqrt{2x-1}+3) }{ (sqrt{2x-1}-3)( sqrt{2x-1}+3)( sqrt{x-1}+2)} = \ = lim_{x to 5} frac{6(x-1-4)}{4(2x-1-9)} = lim_{x to 5} frac{6(x-5)}{8(x-5)} = frac{6}{8} \ 2) ... lim_{x to 0} frac{arctg(8x)*8x}{8x*2x} = lim_{x to 0} frac{8x}{2x}=4$
$3) ... lim_{x to frac{ pi }{2} } frac{ frac{sin3x}{cos3x} }{ frac{sinx}{cosx} }= lim_{x to frac{ pi }{2} } frac{sin3xcosx}{cos3xsinx} = \ = lim_{x to frac{ pi }{2}} frac{-cosx}{cos3x} }=lim_{x to frac{ pi }{2}} frac{sinx}{-3sin3x} = frac{1}{3}$