Developer Personas:
This guide is for developers who want to get a better understanding of the shape of the graph of sin(x) / x.
Overview:
In mathematics, the graph of sin(x)/x is known as the sinc function. This function is an important function in Fourier analysis and has many different applications in engineering and physics. Understanding the shape of thegraph can help developers gain a better understanding of certain mathematical concepts.
Step-by-Step Guide:
Start by plotting the graph of the sinc function.
Notice that the graph rises as x approaches 0, and then as x moves away from zero both to the right and left, the graph declines.
The graph oscillates around the horizontal line y=1 for values close to 0. As it moves away from 0, it oscillates around 0.
At the points +/-π, the graph becomes zero.
As the graph approaches infinity, the graph approaches 0.
FAQ
What are the values for which the graph passes through the horizontal line y = 1?
The graph of sin(x)/x passes through y=1 at the points x= 0.
What is the range of the graph?
The range of the graph of sin(x)/x is -∞ to +∞.
What are the local maxima and minima of the graph?
The local maxima of the graph of sin(x)/x occurs at x = nπ and the local minima occur at x = (n+0.5)π, where n is an integer.
What is the equation of the horizontal asymptote?
The equation of the horizontal asymptote is y=0.
What are the horizontal and vertical asymptotes of this graph?
The horizontal asymptote of the graph is y = 0, and the vertical asymptotes occur at x = +/- π.
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