8. x→∞limx2−3x−4−x−1

Pertanyaan

8. $\style{font-size:14px}{\lim_{x\rightarrow\infty}\sqrt{x^2-3x-4}-x-1}$

Pembahasan Soal:

Menyelesaikan limit dengan cara berikut.

$begin mathsize 14px style limit as x rightwards arrow infinity of square root of a x squared plus b c plus c end root minus square root of p x squared plus q x plus r end root equals open curly brackets table attributes columnalign left end attributes row cell plus infinity space text untuk end text space a greater than p end cell row cell negative infinity text untuk end text space a less than p end cell row cell fraction numerator b minus q over denominator 2 square root of a end fraction space text untuk end text space a equals p end cell end table close end style$

Untuk $begin mathsize 14px style limit as x rightwards arrow infinity of square root of x squared minus 3 x minus 4 end root minus x minus 1 end style$ , diperoleh

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of square root of x squared minus 3 x minus 4 end root minus x minus 1 end cell equals cell limit as x rightwards arrow infinity of square root of x squared minus 3 x minus 4 end root minus square root of open parentheses x plus 1 close parentheses squared end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of x squared minus 3 x minus 4 end root minus square root of x squared plus 2 x plus 1 end root end cell row blank equals cell fraction numerator negative 3 minus 2 over denominator 2 square root of 1 end fraction end cell row blank equals cell negative 5 over 2 end cell end table end style$

Jadi, nilai $undefined$ adalah $begin mathsize 14px style negative 5 over 2 end style$ .

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Umi

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 05 Oktober 2021