Question

Check the continuity of the func.f giveb by f(x)=2x+3 at x=1

Answer 1

To check if a function is at a perticular point,

We have to check if LHL=RHL=f(x)

Here,

LHL

$\lim_{x \to \ 1-} f(x) \\= \lim_{x \to \ 1-} 2x+3\\= \lim_{h \to \ 0} 2(1-h)+3\\=5$

RHL

$\lim_{x \to \ 1+} f(x) \\= \lim_{x \to \ 1+} 2x+3\\= \lim_{h \to \ 0} 2(+h)+3\\=5$

f(1)=2(1)+3=5

Thus at point x=5, LHL=RHL=f(x). Hence the Funtion is continous.

Hopr this helps.................