# What is the greatest integer function?

Greatest integer function is denoted by [x]. This means, the greatest integer less than or equal to x.

If x is an integer, [x]=x If x is a decimal number, then [x]= the integral part of x.

Consider this example- [3.01]=3 This is because the greatest integer less than 3.01 is 3 similarly, [3.99]=3 [3.67]=3 Now, [3]=3 This is where the equality is used. Since, in this example x is an integer itself, the greatest integer less than or equal to x is x itself.

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The greatest integer function, denoted by ( \lfloor x \rfloor ) or sometimes ( \text{floor}(x) ), returns the greatest integer less than or equal to ( x ). For example:

( \lfloor 3.7 \rfloor = 3 )

( \lfloor -2.3 \rfloor = -3 )

It essentially rounds down to the nearest integer.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- How do you identify all horizontal and slant asymptote for #f(x)=(3x^2+1)/(x^2+x+9)#?

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