AP EAMCET2002MathematicsContinuity and Differentiability
If f: R R defined by f(x)= array cc a^2 ^2 x+b^2 ^2 x, & x 0 e^ a x+b , & x>0 array . is a continuous function, then
Options
- Ab=2 |a|
- B2 b= |a|
- Cb= |2 a|
- Db^2= |a|
Correct answer
A. b=2 |a|
Step-by-step solution
We have, aligned & _ h 0 f(0+h)= _ h 0 e^ a h+b =e^b & and _ h 0 f(0-h)= _ h 0 a^2 ^2 h &+b^2 ^2 h=a^2 0 & Thus, e^b=a^2 & b=2 |a| aligned