Limits Continuity And Differentiability Question 20
Question: If the function $ f(x)=[ \frac{{{(x-2)}^{3}}}{a} ]\sin (x-2)+a\cos (x-2), $ [.] denotes the greatest integer function is continuous and differentiable in [4, 6], then
Options:
A) $ a\in [8,64] $
B) $ a\in (0,8] $
C) $ a\in [64,\infty ) $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Since $ [x^{3}] $ is not continuous and differentiable at integral points. So $ f(x) $ is continuous and differentiable in [4, 6] if $ [ \frac{{{(x-2)}^{3}}}{a} ]=0\Rightarrow a\ge 64 $
BETA
