Question

5. Letf:RR defined by
f(x)=
2x-1 if x <3
5 if x>3
Then show that. Lt f(x) = 5
Stowa
x →3
please solve this​

Answer 1

Step-by-step explanation:

We have,

$\: \: \: \: \: \: \: \: \: \: \: f(x) = \{ 2x - 1 \: \: if \: \: x < 3 \\ f(x) = \{5 \: \: if \:\: x \geqslant 3$

LHL :

$\lim_{h \rarr0} \: f(3 - h)$

$= \lim _{h \rarr0}2(3 - h) - 1$

$= 2(3 - 0) - 1 = 6 - 1 = 5$

RHL :

$\lim_{h \rarr0} f(3 + h)$

$= 5$

Hence,

$\lim_{x \rarr3} f(x) = 5$