How do you graph #y=5csc3(xpi)5#?
As below.
graph{5 csc(3x  3 pi)  5 [10, 10, 5, 5]}
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To graph (y = 5\csc(3(x  \pi))  5), follow these steps:

Identify the vertical asymptotes: Set the expression inside the cosecant function equal to zero and solve for (x). [3(x  \pi) = 0 ] [x  \pi = 0 ] [x = \pi ]

Plot the vertical asymptote at (x = \pi).

Determine the amplitude of the graph, which is the absolute value of the coefficient of the cosecant function, (5).

Graph the cosecant function: Start by plotting key points of the cosecant function, which occur at the zeros of the sine function. For (y = \csc(x)), these occur at multiples of (\pi). [x_1 = \pi  \pi = 0 ] [x_2 = \pi + \pi = 2\pi ] [x_3 = \pi + 2\pi = 3\pi ] [x_4 = \pi  2\pi = \pi ] [x_5 = \pi  3\pi = 2\pi ]

Plot these points and draw the curve. Remember that the graph approaches the asymptotes but never crosses them.

Multiply the graph of the cosecant function by the amplitude, (5), and then subtract (5) to shift the graph downward.

Label the graph as necessary.

Your final graph should resemble the general shape of the cosecant function, but it will be vertically stretched by a factor of (5) and shifted downward by (5).
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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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