Question

3. Sketch the graph of the following function:
2 + 1 < 3
f(x) = { 5 = 3 −5 ≤ x ≤ 5 With an intervals of 0.5. 6 > 3
Find lim ()
→3

Answer 1

We have,

f(x)={2x+3,3(x+1)x≤0x≥0

For the first case:

L.H.L:  x→0−limf(x)=x→0−lim(2x+3)=2×0+3=3

R.H.L:  x→0+limf(x)=x→0+lim3(x+1)=3(0+1)=3

So, x→0limf(x) exists and is equal to 3

For the second case:

L.H.L:  x→1−limf(x)=x→1−lim2x+3=2×1+3=5

R.H.L:  x→1+limf(x)=x→1+lim3(x+1)=3(1+1)=6

Since, x→1−limf(x)=x→1+limf(x)

Hence, x→1−limf(x) does not exist.