Lim X→∞ (√3x - 5) (√2x + 1 )= ......

Lim X→∞ (√3x – 5) (√2x + 1 )= ……

Jawab:

Kategori Soal : Matematika – Limit Trigonometri

Kelas : 2 SMA/XI SMA

Pembahasan :

Jawaban terlampir

Gambar Jawaban

Jawab:

Limit = ∞

Penjelasan dengan langkah-langkah:

$displaystyle t(x) = sqrt{3x-5} -sqrt{2x+1}\t^2(x) = 3x-5+2x+1 - 2cdot sqrt{3x-5cdot}sqrt{2x+1}\t(x) = sqrt{5x-4 - 2sqrt{6x^2-7x-5}}\lim_{xto infty}t(x) = lim_{xto infty}( sqrt{3x-5} -sqrt{2x+1}) = lim_{xto infty} sqrt{5x-4 - 2sqrt{6x^2-7x-5}}$

$displaystyle lim_{xto infty}( sqrt{3x-5} -sqrt{2x+1}) = lim_{xto infty} sqrt{5x-4 - 2sqrt{6left(x-frac{7}{12}right)^2 -6cdot left(frac{7}{12} right)^2-5 }}\lim_{xto infty}( sqrt{3x-5} -sqrt{2x+1}) approx lim_{xto infty} sqrt{5x-4 - 2sqrt{6left(x-frac{7}{12}right)^2 }}$

$displaystyle lim_{xto infty}( sqrt{3x-5} -sqrt{2x+1}) approx lim_{xto infty} sqrt{5x-4 - 2sqrt{6} cdot left(x-frac{7}{12} right) }\lim_{xto infty}( sqrt{3x-5} -sqrt{2x+1}) approx lim_{xto infty} sqrt{5x-4 - 2sqrt{6} x+ frac{7}{6}sqrt{6} } \\huge{boxed{boxed{boldsymbol{lim_{xto infty}( sqrt{3x-5} -sqrt{2x+1}) = infty}}}$

Gambar Jawaban