Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

If the function $ f(x) = \left\{ \begin{array}{l l} 3ax+b & \quad for \quad x > 1 \\ 11 & \quad for \quad x = 1 \\ 5ax-2b & \quad for \quad x < 1 \end{array} \right. $ is continuous at $x=1$.find the values of a and b .

$\begin{array}{1 1}(A)\;a=4\;b=2 \\(B)\;a=3\;b=2 \\(C)\;a=0\;b=1 \\(D)\;a=3\;b=6 \end{array}$

Can you answer this question?

1 Answer

0 votes
We have $f(1)=11$
$\lim \limits_{x \to 1+} f(x) =\lim \limits_{h \to 0} f(1+h)$
$\qquad= \lim \limits_{h \to 0} \{ 3a(1+h) +b\}$
$\qquad= \lim \limits_{h \to 0} \{ (3a+b) +3ah \}$
$\qquad= (3a+b)$
$\lim \limits_{x \to 1-} f(x) =\lim \limits_{h \to 0} f(1-h)$
$\qquad= \lim \limits_{h \to 0} \{ 5a(1-h) -2b \}$
$\qquad= \lim \limits_{h \to 0} \{ (5a-2b) -5ah \}$
$\qquad= (5a-2b)$
Since $f(x)$ is continuous at $x=1$ we have
$\lim \limits_{x \to {1+}} f(x)=\lim \limits_{x \to {1-}}=f(1)$
$\qquad 11a=33$
$\qquad a=3$
$3 \times 3 +b =11$
$9 +b=11$
Hence B is the correct answer.
answered Apr 22, 2014 by meena.p

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App