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Question

If l(x) is the least integer not less than x and g(x) is the greatest integer not greater than x, then limxe+πl(x)+g(x)=?


A

9

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B

13

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C

1

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D

None of these

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Solution

The correct option is D

None of these


Explanation for the correct option:

It is given that,

l(x) least integer x, and

g(x) greatest integer x

Now it is given that for the limit x tends to e+π

So, we know that, e=2.71,π=3.14

Thus, x=e+π=5.85

For, l(x)=l(5.85), the least integer will be 6

and for, g(x)=g(5.85), the greatest integer will be 5.

Thus,

l(x)+g(x)=5+6=11

Therefore, the correct option is (D), “None of these”.


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