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

Answer 1

Lily Anderson

We can rewrite this as follows

#f(x)=(x)/[absxsqrt(1+1/x^2)]#

Hence for #x->+oo# we have that #f(x)->1#

and

for #x->-oo# we have that #f(x)->-1#

Hence the horizontal asympotes are #y=1# and #y=-1#

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Answer 2

Madelyn Anderson

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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Answer from HIX Tutor

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.