First slide

Continuity

Question

$\begin{matrix} f (x) = \{\begin{array}{cl} (\frac{3}{x^{2}}) \sin 2 x^{2} & if x < 0 \\ \frac{x^{2} + 2 x + c}{1 - 3 x^{2}} & if x \geq 0, x \neq \frac{1}{\sqrt{3}} then in order that f be continuous at x = 0 then \\ 0 & if x = \frac{1}{\sqrt{3}} \end{array} \end{matrix} the value of c is$

Moderate

A

2
B

4
C

6
D

8

Solution

$\underset{x = 0^{-}}{L t} f (x) = \underset{x = 0^{-}}{L t} \frac{3}{x^{2}} \sin 2 x^{2} = 6 \underset{x \to 0}{L t} \frac{\sin 2 x^{2}}{2 x^{2}} = 6$
$\underset{x = 0^{+}}{L t} f (x) = \underset{x = 0^{+}}{L t} \frac{x^{2} + 2 x + c}{1 - 3 x^{2}} = \frac{c}{1} = c$
$∴ f is continuous ∴ c = 6$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App