Answer:
Hence, the limit of the expression is:
-0.5 (i.e. option:d is correct)
Step-by-step explanation:
We have to evaluate the limit of the expression:
[tex]\lim_{x \to 0} \dfrac{\sqrt{1-x}-1}{x}[/tex]
We know that the numerator and denominator both are equal to zero on putting x=0 hence we get a 0/0 form and hence we apply L'hospitals rule.
i.e. we differentiate the numerator and denominator term and then apply the limit.
We know that on differentiating the numerator we get:
[tex]\dfrac{-1}{2\sqrt {1-x}}[/tex]
and on differentiating the denominator we get:
1
Hence, we need to find the limit of the expression:
[tex]\lim_{x \to 0} \dfrac{-1}{2\sqrt{1-x}}\\\\=\dfrac{-1}{2\sqrt{1-0}}\\\\=\dfrac{-1}{2}\\\\=-0.5[/tex]
Hence, the limit of the expression is:
-0.5
