Bantu dong nyari limitnya

Bantu dong nyari limitnya

$red{bold{1.}}$

$lim_{xtoinfty}~frac{4x^2~-~3}{x^2~+~4x~-~5}$

$=lim_{xtoinfty}~frac{frac{4x^2~-~3}{x^2}}{frac{x^2~+~4x~-~5}{x^2}}$

$=lim_{xtoinfty}~frac{4~-~frac{3}{x^2}}{1~+~frac{4}{x}~-~frac{5}{x^2}}$

$=~frac{4~-~frac{3}{infty^2}}{1~+~frac{4}{infty}~-~frac{5}{infty^2}}$

$=~frac{4~-~0}{1~+~0~-~0}$

$boxed{boxed{lim_{xtoinfty}~frac{4x^2~-~3}{x^2~+~4x~-~5}~=~4}}$

$red{bold{2.}}$

$lim_{xtoinfty}~frac{(2x~-~1)^2}{x~+~5}$

$=lim_{xtoinfty}~frac{4x^2~-~4x~+~1}{x~+~5}$

$=lim_{xtoinfty}~frac{frac{4x^2~-~4x~+~1}{x^2}}{frac{x~+~5}{x^2}}$

$=lim_{xtoinfty}~frac{4~-~frac{4}{x}~+~frac{1}{x^2}}{frac{1}{x}~+~frac{5}{x^2}}$

$=~frac{4~-~frac{4}{infty}~+~frac{1}{infty^2}}{frac{1}{infty}~+~frac{5}{infty^2}}$

$=~frac{4~-~0~+~0}{0~+~0}$

$boxed{boxed{lim_{xtoinfty}~frac{(2x~-~1)^2}{x~+~5}=~+infty}}$

$red{bold{3.}}$

$lim_{xtoinfty}~frac{x^2~-~12x~+~6}{sqrt{16x^9~-~1}}$

$=~lim_{xtoinfty}~frac{frac{x^2~-~12x~+~6}{x^3}}{frac{sqrt{16x^9~-~1}}{x^3}}$

$=~lim_{xtoinfty}~frac{frac{x^2~-~12x~+~6}{x^3}}{sqrt{frac{16x^9~-~1}{x^9}}}$

$=~lim_{xtoinfty}~frac{frac{1}{x}~-~frac{12}{x^2}~+~frac{6}{x^3}}{sqrt{16~-~frac{1}{x^9}}}$

$=~frac{frac{1}{infty}~-~frac{12}{infty^2}~+~frac{6}{infty^3}}{sqrt{16~-~frac{1}{infty^9}}}$

$=~frac{0~-~0~+~0}{sqrt{16~-~0}}$

$boxed{boxed{lim_{xtoinfty}~frac{x^2~-~12x~+~6}{sqrt{16x^9~-~1}}~=~0}}$

$red{bold{4.}}$

$lim_{xtoinfty}~(sqrt{x~-~4}~-~sqrt{x~+~2})$

$=~lim_{xtoinfty}~(sqrt{x~-~4}~-~sqrt{x~+~2}~times~frac{sqrt{x~-~4}~+~sqrt{x~+~2}}{sqrt{x~-~4}~+~sqrt{x~+~2}})$

$=~lim_{xtoinfty}~(frac{(sqrt{x~-~4})^2~-~(sqrt{x~+~2})^2}{sqrt{x~-~4}~+~sqrt{x~+~2}})$

$=~lim_{xtoinfty}~(frac{(x~-~4)~-~(x~+~2)}{sqrt{x~-~4}~+~sqrt{x~+~2}})$

$=~lim_{xtoinfty}~(frac{-6}{sqrt{x~-~4}~+~sqrt{x~+~2}})$

$=~lim_{xtoinfty}~(frac{frac{-6}{sqrt{x}}}{frac{sqrt{x~-~4}~+~sqrt{x~+~2}}{sqrt{x}}})$

$=~lim_{xtoinfty}~(frac{frac{-6}{sqrt{x}}}{sqrt{frac{x~-~4}{x}}~+~sqrt{frac{x~+~2}{x}}})$

$=~lim_{xtoinfty}~(frac{frac{-6}{sqrt{x}}}{sqrt{1~-~frac{4}{x}}~+~sqrt{1~+~frac{2}{x}}})$

$=~frac{frac{-6}{sqrt{infty}}}{sqrt{1~-~frac{4}{infty}}~+~sqrt{1~+~frac{2}{infty}}}$

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

$boxed{boxed{lim_{xtoinfty}~(sqrt{x~-~4}~-~sqrt{x~+~2})~=~0}}$

$red{bold{5.}}$

$lim_{xtoinfty}~(sqrt{x^2~-~x~+~4}~-~sqrt{x^2~+~x~-~2})$

$=~lim_{xtoinfty}~(sqrt{x^2~-~x~+~4}~-~sqrt{x^2~+~x~-~2}~times~frac{sqrt{x^2~-~x~+~4}~+~sqrt{x^2~+~x~-~2}}{sqrt{x^2~-~x~+~4}~+~sqrt{x^2~+~x~-~2}})$

$=~lim_{xtoinfty}~(frac{(sqrt{x^2~-~x~+~4})^2~-~(sqrt{x^2~+~x~-~2})^2}{sqrt{x^2~-~x~+~4}~+~sqrt{x^2~+~x~-~2}})$

$=~lim_{xtoinfty}~(frac{(x^2~-~x~+~4)~-~(x^2~+~x~-~2)}{sqrt{x^2~-~x~+~4}~+~sqrt{x^2~+~x~-~2}})$

$=~lim_{xtoinfty}~(frac{-2x~+~6}{sqrt{x^2~-~x~+~4}~+~sqrt{x^2~+~x~-~2}})$

$=~lim_{xtoinfty}~(frac{frac{-2x~+~6}{x}}{frac{sqrt{x^2~-~x~+~4}~+~sqrt{x^2~+~x~-~2}}{x}})$

$=~lim_{xtoinfty}~(frac{frac{-2x~+~6}{x}}{sqrt{frac{x^2~-~x~+~4}{x^2}}~+~sqrt{frac{x^2~+~x~-~2}{x^2}}})$

$=~lim_{xtoinfty}~(frac{-2~+~frac{6}{x}}{sqrt{1~-~frac{1}{x}~+~frac{4}{x^2}}~+~sqrt{1~+~frac{1}{x}~-~frac{2}{x^2}}})$

$=~frac{-2~+~frac{6}{infty}}{sqrt{1~-~frac{1}{infty}~+~frac{4}{infty^2}}~+~sqrt{1~+~frac{1}{infty}~-~frac{2}{infty^2}}}$

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

$boxed{boxed{lim_{xtoinfty}~(sqrt{x^2~-~x~+~4}~-~sqrt{x^2~+~x~-~2})~=~-1}}$

#limit tak hingga

Jawaban:

nomor satu jawabannya 4 * 2 = 8 dikurang 3 = 5 5 lalu dikalikan 2 = 10 + 4 = 14 lalu dikali lima = 70 dikurang 5 = 65