COMPUTER EXPLORATIONSUse a CAS to perform the
Chapter 3, Problem 50E(choose chapter or problem)
Use a CAS to perform the following steps for the functions in Exercises 49-52.
a. Plot \(y=f(x)\) over the interval \(\left(x_{0}-1 / 2\right) \leq x \leq\left(x_{0}+3\right)\).
b. Holding \(x_{0}\) fixed, the difference quotient
\(q(h)=\frac{f\left(x_{0}+h\right)-f\left(x_{0}\right)}{h}\)
at \(x_{0}\) becomes a function of the step size \(h\). Enter this function into your CAS workspace.
c. Find the limit of \(q\) as \(h \rightarrow 0\).
d. Define the secant lines \(y=f\left(x_{0}\right)+q \cdot\left(x-x_{0}\right)\) for \(h=\) 3, 2, and 1 . Graph them together with \(f\) and the tangent line over the interval in part (a).
\(f(x)=x+\frac{5}{x},\quad\ \ \ x_0=1\)
Equation Transcription:
Text Transcription:
y=f(x)
(x_0 - 1/2) leq x leq (x_0 + 3)
x_0
q(h) = f(x_0 + h) - f(x_0) / h
x_0
h
q
h rightarrow 0
y = f(x_0) + q cdot (x - x_0)
h=
f
f(x) = x + 5/x, x_0 = 1
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