## Question

###### In the limit #lim sqrtx=0# as #x->0^+#, how do you find #delta>0# such that whenever #0<x<delta#, #sqrtx<0.01#?

In the limit #lim sqrtx=0# as #x->0^+#, how do you find #delta>0# such that whenever #0

## Answers

As

#y=sqrtx# is a strictly increasing function:

#0 < x < epsilon^2 <=> 0 < sqrt(x) < sqrt(epsilon^2)# So, for any

#epsilon > 0# , if we take#delta_epsilon = epsilon^2# we have:

#0 < x < delta_epsilon <=> 0 < sqrt(x) < epsilon# In particular for

#epsilon =0.01# we can choose#delta_epsilon <= 0.0001#

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