Bantu jawab dong kak pake caranya

By Admin ReiPosted on October 29, 2022

Bantu jawab dong kak pake caranya

Bantu jawab dong kak pake caranya

$boxed{bold{3.}}$

$lim_{~xto~infty}(sqrt{x-sqrt{x}}-sqrt{x+sqrt{x}})$

$=lim_{~xto~infty}(sqrt{x-sqrt{x}}-sqrt{x+sqrt{x}})times frac{sqrt{x-sqrt{x}}+sqrt{x+sqrt{x}}}{sqrt{x-sqrt{x}}+sqrt{x+sqrt{x}}})$

$=lim_{~xto~infty}(frac{(sqrt{x-sqrt{x}})^2-(sqrt{x+sqrt{x}})^2}{sqrt{x-sqrt{x}}+sqrt{x+sqrt{x}}})$

$=lim_{~xto~infty}(frac{(x-sqrt{x})-(x+sqrt{x})}{sqrt{x-sqrt{x}}+sqrt{x+sqrt{x}}})$

$=lim_{~xto~infty}(frac{x-sqrt{x}-x-sqrt{x}}{sqrt{x-sqrt{x}}+sqrt{x+sqrt{x}}})$

$=lim_{~xto~infty}(frac{-2sqrt{x}}{sqrt{x-sqrt{x}}+sqrt{x+sqrt{x}}})$

$=lim_{~xto~infty}(frac{frac{-2sqrt{x}}{sqrt{x}}}{frac{sqrt{x-sqrt{x}}+sqrt{x+sqrt{x}}}{sqrt{x}}})$

$=lim_{~xto~infty}(frac{frac{-2sqrt{x}}{sqrt{x}}}{sqrt{frac{x-sqrt{x}}{x}}+sqrt{frac{x+sqrt{x}}{x}}})$

$=lim_{~xto~infty}(frac{-2}{sqrt{1-frac{1}{sqrt{x}}}+sqrt{1+frac{1}{sqrt{x}}}})$

$=frac{-2}{sqrt{1-frac{1}{sqrt{infty}}}+sqrt{1+frac{1}{sqrt{infty}}}}$

$=frac{-2}{sqrt{1-0}+sqrt{1+0}}==frac{-2}{1+1}$

$boxed{boxed{lim_{~xto~infty}(sqrt{x-sqrt{x}}-sqrt{x+sqrt{x}})=-1}}$

$boxed{bold{4.}}$

$lim_{~xto~infty}(3x+1-sqrt{9x^2+4x-7})$

$=lim_{~xto~infty}(3x+1-sqrt{9x^2+4x-7}times frac{3x+1+sqrt{9x^2+4x-7}}{3x+1+sqrt{9x^2+4x-7}})$

$=lim_{~xto~infty}(frac{(3x+1)^2-(sqrt{9x^2+4x-7})^2}{3x+1+sqrt{9x^2+4x-7}})$

$=lim_{~xto~infty}(frac{(9x^2+6x+1)-(9x^2+4x-7)}{3x+1+sqrt{9x^2+4x-7}})$

$=lim_{~xto~infty}(frac{9x^2+6x+1-9x^2-4x+7}{3x+1+sqrt{9x^2+4x-7}})$

$=lim_{~xto~infty}(frac{2x+8}{3x+1+sqrt{9x^2+4x-7}})$

$=lim_{~xto~infty}(frac{frac{2x+8}{x}}{frac{3x+1+sqrt{9x^2+4x-7}}{x}})$

$=lim_{~xto~infty}(frac{frac{2x+8}{x}}{frac{3x+1}{x}+sqrt{frac{9x^2+4x-7}{x^2}}})$

$=lim_{~xto~infty}(frac{2+frac{8}{x}}{3+frac{1}{x}+sqrt{9+frac{4}{x}-frac{7}{x^2}}})$

$=frac{2+frac{8}{infty}}{3+frac{1}{infty}+sqrt{9+frac{4}{infty}-frac{7}{infty^2}}}$

$=frac{2+0}{3+0+sqrt{9+0-0}}=frac{2}{3+3}$

$boxed{boxed{lim_{~xto~infty}(3x+1-sqrt{9x^2+4x-7})=frac{1}{3}}}$

$boxed{bold{5.}}$

$lim_{~xto~infty}(2+~cos~frac{4}{x})$

$=lim_{~xto~infty}~2~+~lim_{~xto~infty}~cos~frac{4}{x}$

$=2~+~cos~frac{4}{infty}$

$=2~+~cos~0=2+1$

$boxed{boxed{lim_{~xto~infty}(2+~cos~frac{4}{x})=3}}$