# How do you find intercepts, extrema, points of inflections, asymptotes and graph #y=x/(x^2+1)#?

graph{x/(x^2+1) [-10, 10, -1, 1]}

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To find the intercepts, set ( y = 0 ) and solve for ( x ). For extrema, differentiate the function, set the derivative equal to zero, and solve for ( x ). To find points of inflection, differentiate the function twice, set the second derivative equal to zero, and solve for ( x ). To find asymptotes, determine the horizontal asymptote by analyzing the behavior of the function as ( x ) approaches positive or negative infinity, and vertical asymptotes by finding values of ( x ) that make the denominator of the function equal to zero. To graph ( y = \frac{x}{x^2 + 1} ), plot intercepts, extrema, points of inflection, asymptotes, and sketch the curve accordingly.

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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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