COMPUTER EXPLORATIONSUse a CAS to perform the

Chapter 3, Problem 52E

(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).

\(f(x)=\cos x+4\sin(2x),\quad\ \ \ x_0=\pi\)

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) = cos x + 4 sin(2x),   x_0 = pi