# How do you find the domain of the function #F(x) = (x^2+3x+4)/(x^2+1)^(1/2)#?

"Note that for all real values of x, sqrt(x^2+1)>0."

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To find the domain of the function ( F(x) = \frac{x^2+3x+4}{\sqrt{x^2+1}} ), we need to consider the values of ( x ) for which the function is defined.

Since the square root function ( \sqrt{x} ) is defined only for non-negative values of ( x ), the denominator ( \sqrt{x^2+1} ) is defined for all real numbers. However, the numerator ( x^2+3x+4 ) is a quadratic polynomial which is defined for all real numbers ( x ).

Therefore, the domain of the function ( F(x) ) is all real numbers ( x ).

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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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