Denition approach of learning new topics

18 3 EXAMPLES OF WHAT IS A LIMIT?
{
1 x ≥ 0
(c) f(x) =
−1 x < 0 at x = 0
Now will we just nd limit here without trying to see what is the
RHL and LHL??
Here we have to nd the LHL and RHL separately and check if both
are equal. If both are equal then the function has limits at x = 0 or
else it doesnt have a limit.
RHL = lim
x→0 + f(x)
= lim 1
x→0 +
(since right of 0 f(x) = 1)
= 1
LHL = lim
x→0 − f(x)
= lim (−1)
x→0 − (since left of 0 f(x) = −1)
= −1
And we see that LHL ≠ RHL
Hence the limits doesnt exist in this case.
3.8 Practise Problems in Limits
1. lim
x→0 + sin x
|x|
2. lim
θ→0
tan θ
θ
(Solution : 1)
(Solution : 1)
3. Find the anwers to the following functions, given D f : [0, 3] and is represented
in the adjoining gure
(a) f(1)