How do you graph of the function #y=arctan(x)#?
If we create a table of typical
and then modify the labels:
Plot the (modified label) table
and you should get something like:
graph{arctan(x) [6.24, 6.247, 3.12, 3.12]}
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To graph the function y = arctan(x), follow these steps:

Identify the key points:
 The function approaches π/2 as x approaches negative infinity.
 The function approaches π/2 as x approaches positive infinity.
 The function passes through the point (0, 0), as arctan(0) = 0.

Draw the asymptotes:
 There are vertical asymptotes at x = ∞ and x = +∞ due to the behavior of the function as x approaches these values.

Plot the key points:
 Plot the point (0, 0) as it is the yintercept.

Draw the curve:
 The curve starts from negative infinity, approaches the yaxis from below, passes through the point (0, 0), and then approaches positive infinity while getting closer to the asymptote at y = π/2.

Sketch the curve smoothly, keeping in mind its behavior as described above.

Label the axes and any important points as necessary.
This results in a curve that starts near the origin, approaches the yaxis without touching it, and continues upward toward positive infinity. The curve never exceeds the range π/2 to π/2 on the yaxis.
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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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 How do you find all critical point and determine the min, max and inflection given #f(x)=3x^24x+1#?
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