Answer:
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 indeterminant 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)^1/4
Now we can apply the limit
lim -1/2(1 - x)^1/4 = -1/2 (1-0)^1/4
= -1 / 2(1)^1/4
= -1/2
= -0.5
Hope you understand the concept.
Thank you.
x-->0