How do you graph of the function #y=arctan(x)#?
If we create a table of typical
Plot the (modified label) table graph{arctan(x) [-6.24, 6.247, -3.12, 3.12]}
and then modify the labels:
and you should get something like:
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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 y-intercept.
-
Draw the curve:
- The curve starts from negative infinity, approaches the y-axis 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 y-axis without touching it, and continues upward toward positive infinity. The curve never exceeds the range -π/2 to π/2 on the y-axis.
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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.
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.
- For what values of x is #f(x)=(2x-2)(x-4)(x-3)# concave or convex?
- What are the points of inflection, if any, of #f(x) = x^5/20 - 5x^3 + 5 #?
- How do you find concavity, inflection points, and min/max points for the function: #f(x)=x(x^2+1)# defined on the interval [–5,4]?
- How do you find the local maximum and minimum values of #f(x)=2x^3 + 5x^2 - 4x - 3#?
- How do you sketch the graph by determining all relative max and min, inflection points, finding intervals of increasing, decreasing and any asymptotes given #f(x)=(x-4)^2/(x^2-4)#?

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