The table below records selected values of a function for near

MATHEMATICS · Multi-part · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

The table below records selected values of a function

p

for

x

near

4

, but not at

x=4

$x$	$3.70$	$3.80$	$3.90$	$3.99$	$4.01$	$4.10$	$4.20$	$4.30$
$p(x)$	$1.28$	$1.23$	$1.20$	$1.19$	$2.81$	$2.86$	$2.90$	$2.93$

Use these data to study the behaviour of

p

x=4

. (i) Estimate

\displaystyle \lim_{x\to 4^-} p(x)

and

\displaystyle \lim_{x\to 4^+} p(x)

. (ii) Do you expect

\displaystyle \lim_{x\to 4} p(x)

to exist? Give a clear reason based on the estimates obtained. (iii) Suppose it is later found that

p(4)=2.00

. Does this information alter your conclusion in part (ii)? Explain briefly.