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  • If the function <img alt="\mathrm{ f(x)=\left[\frac{(x-5)^3}{A}\right] \sin (x-5)+a \cos (x-2) }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%20f%28x%29%3D%5Cleft%5B%5Cfrac%7B

If the function \mathrm{ f(x)=\left[\frac{(x-5)^3}{A}\right] \sin (x-5)+a \cos (x-2) }, where \mathrm{[\cdot] } denotes the greatest integer function, is continuous in (7,9), then least value of A is

Option: 1

63


Option: 2

65


Option: 3

66


Option: 4

64


Answers (1)

As [x] is not continuous at integral values.
So, f(x) is continuous in (7,9) if \mathrm{\left[\frac{(x-5)^3}{A}\right]=0}

\mathrm{\Rightarrow A \geq(9-5)^3 \Rightarrow A \geq 64 \quad \therefore A \in[64, \infty)}
 

Posted by

Kshitij

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