First slide

Continuity

Question

$If f (x) = \frac{acosx - cosbx}{x^{2}}, x \neq 0 and f (0) = 4$ is continuous at x=0, then the ordered pair (a, b) is

Moderate

A

$(\pm 1, 3)$
B

$(1, \pm 3)$
C

$(- 1, - 3)$
D

$(1, 3)$

Solution

$\begin{array}{l} We must have \lim_{x \to 0} \frac{acosx - cosbx}{x^{2}} = 4 \\ or \lim_{x \to 0} \frac{a (1 - \frac{x^{2}}{2!}) - (1 - \frac{b^{2} x^{2}}{2!})}{x^{2}} = 4 \\ or \lim_{x \to 0} [\frac{(a - 1)}{x^{2}} - (\frac{a}{2} - \frac{b^{2}}{2})] = 4 \\ or a = 1 and \frac{a}{2} - \frac{b^{2}}{2} = - 4 \\ or a = 1 and b^{2} = 9 \\ or a = 1 and b = \pm 3 \end{array}$

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