Answer: Area The area between the graph of the function and the axis over the interval

Chapter 5, Problem 100

(choose chapter or problem)

The area A between the graph of the function

g(t)=4-\frac{4}{t^{2}}

and the t-axis over the interval \([1, x]\) is

\(A(x)=\int_{1}^{x}\left(4-\frac{4}{t^{2}}\right) d t\)

(a) Find the horizontal asymptote of the graph of g.

(b) Integrate to find A as a function of x. Does the graph of A have a horizontal asymptote? Explain.

Text Transcription:

g(t)=4-\frac 4 t^2

[1, x]

A(x)=\int_1^x(4-\frac 4 t^2) d t

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