Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability
Let f(x)=e^ -1 x^2 + ₀^ x 2 1+ t d t x (0, ) , then:
Options
- Af^ (x) exist and is continuous x (0, )
- Bf^ (x) exist x (0, )
- Cf^ (x) is bounded
- Dthere exist >0 such that |f(x)|> |f^ (x) | x ( , )
Correct answer
D. there exist >0 such that |f(x)|> |f^ (x) | x ( , )
Step-by-step solution
f^ (x)=e^ -1 x^2 ( 2 x^3 )+ 1+ x 2 ( 2 ) (A) Also f^ (x) is bounded but f(x) is unbound because _ x f(x) Also f^ (x) does not exist at 3,7,11 . (d) is obvious.