How do you sketch the curve #y=x^2+1/x# by finding local maximum, minimum, inflection points, asymptotes, and intercepts?
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To sketch the curve (y = x^2 + \frac{1}{x}) and find its local maximum, minimum, inflection points, asymptotes, and intercepts:

Intercepts:
 xintercept: Set (y = 0) and solve for (x).
 yintercept: Set (x = 0) and solve for (y).

Asymptotes:
 Horizontal asymptote: As (x) approaches positive or negative infinity, (y) approaches the horizontal asymptote, which is determined by the highest power term in the expression.
 Vertical asymptotes: Set the denominator of the rational expression equal to zero and solve for (x).

Local Maximum and Minimum:
 Take the derivative of (y) with respect to (x) and find critical points by setting the derivative equal to zero and solving for (x).
 Use the second derivative test to classify the critical points as local maxima, minima, or points of inflection.

Inflection Points:
 Find the second derivative of (y) with respect to (x).
 Set the second derivative equal to zero and solve for (x) to find points of inflection.

Sketch the Curve:
 Use the information obtained above to sketch the curve, including intercepts, asymptotes, and critical points.
Follow these steps systematically to sketch the curve and locate the desired points.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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