Question

Estimate the limit.
Picture below

Answer 1

d. lim f(x) = -0.5

x-->0

Explanation:

Given:

lim [√(1 - x) - 1] / x

x -->0

When we directly substitute the limit x =0, we get

= 0/0 which is indeterminate form.

Now we have to use the L'hospital rule.

This is nothing but we need to differentiate the numerator and the denominator and apply the limit

d/dx (√1 - x) - 1= 1/2(√1 - x)^-1/2 (-1)

= -1/2√(1 - x)

Now we can apply the limit

lim -1/2(1 - x)^1/2 = -1/2 (1-0)^1/2

= -1 / 2(1)^1/2

= -1/2

= -0.5

Hope you understand the concept.

Thank you.