# How do you find the asymptotes for #f(x) = x / sqrt(x^2 + 1)#?

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To find the asymptotes for ( f(x) = \frac{x}{\sqrt{x^2 + 1}} ), first identify vertical asymptotes by setting the denominator equal to zero and solving for ( x ). There are no vertical asymptotes for this function. Next, find the horizontal asymptote by examining the behavior of the function as ( x ) approaches positive or negative infinity. The horizontal asymptote is ( y = 0 ).

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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.

- How do you find vertical, horizontal and oblique asymptotes for #f(x) = (2x^2 +x -1) /( x-1)#?
- How do you find the asymptotes for #f(x) = (3x )/ (x+4)#?
- How do you find the vertical, horizontal or slant asymptotes for #m(x) = (1-x^2)/(x^3)#?
- How do you find the inverse of #f(x) = log 2^x#?
- How do you find the vertical, horizontal or slant asymptotes for #((x-1)(x-3))/(x(x-2) )#?

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