Mathematics

Problem

The table shows values of a function

f

near

x=1

x	0.90	0.99	1.01	1.10
f(x)	2.97	2.997	3.003	3.030

Determine the constant

k

such that

\displaystyle \lim_{x\to 1} k\,f(x)=15

. Give your answer as an exact numerical value.