Question

Estimate the limit. √1-x -1/x

Answer 1

Answer:

d) lim  f(x) = -0.5

x---> 0

Step-by-step 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