Question

Estimate the limit.

Picture below

Answer 1

Hence, the limit of the expression is:

-0.5 (i.e. option:d is correct)

Explanation:

We have to evaluate the limit of the expression:

`\lim_(x \to 0) (√(1-x)-1)/(x)`

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:

`\frac{-1}{2\sqrt {1-x}}`

and on differentiating the denominator we get:

1

Hence, we need to find the limit of the expression:

`\lim_(x \to 0) (-1)/(2√(1-x))\\\\=(-1)/(2√(1-0))\\\\=(-1)/(2)\\\\=-0.5`

Hence, the limit of the expression is:

-0.5