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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
The value of $\mathop {\lim }\limits_{x \to - \infty } \frac{{\sqrt {4{x^2} + 5x + 8} }}{{4x + 5}} $ is
  • ✓
    $ - 1/2$
  • B
    $0$
  • C
    $1/2$
  • D
    $1$
✓

Answer

Correct option: A.
$ - 1/2$
a
(a) $\mathop {\lim }\limits_{x\, \to \, - \infty } \,\frac{{\sqrt {4{x^2} + 5x + 8} }}{{4x + 5}}$

$ = \mathop {\lim }\limits_{h \to 0} \,\,\frac{{\sqrt {4\,{{( - 1/h)}^2} + 5\,( - 1/h) + 8} }}{{4\,( - 1/h) + 5}}$

$ = \mathop {\lim }\limits_{h \to 0} \,\,\frac{{(1/h)\sqrt {4\, - 5h + 8{h^2}} }}{{(1/h)\,( - \,4 + 5h)}} = \frac{{\sqrt 4 }}{{ - 4}} = - \frac{1}{2}$.

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