Discuss the continuity of the function f(x)={x2−3xifx&lt;22x+4ifx≥2 on the open interval 0≤x≤2

"Discuss the continuity of the function f(x)={x2−3xifx<22x+4ifx≥2 on..." was answered by our community

abondantQ

Answered question

2021-11-06

Discuss the continuity of the function $f (x) = {\begin{cases} x^{2} - 3 x & i f & x < 2 \\ 2 x + 4 & i f & x \geq 2 \end{cases}$
on the open interval $0 \leq x \leq 2$

Answer & Explanation

Benedict

Skilled2021-11-07Added 108 answers

Here, function f(x) is,
$f (x) = {\begin{cases} x^{2} - 3 x & i f & x < 2 \\ 2 x + 4 & i f & x \geq 2 \end{cases}$
In the open interval, 0 The function will be, $f (x) = x^{2} - 3 x$
As f(x) is the quadratic function. Thus, it is continuous.
In the closed interval, 0 Check its continuity at x=2.
Determine the left hand limit, LHL and Right hand limit(RHL).
$L H L = lim_{x \to 2^{-}} f (x)$
$= lim_{x \to 2^{-}} x^{2} - 3 x$
$= 2^{2} - 3 (2)$
$= - 2$
$R H L = lim_{x \to 2^{+}} f (x)$
$= lim_{x \to 2^{+}} 2 x + 4$
$= 2 (2) + 4$
$= 8$
As, $L H L \neq R H L$ .
The function is not continuous at x=2.
Hence, the function is not continuous in $0 < x \leq 2$

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 1

Didn't find what you were looking for?