Limits and Derivatives: MATLAB Assignment

1. Try the following commands:

syms x h
f = x3 + x2 + x + 1
m = (subs(f, x+h)-f)/h
f1 = limit(m, h, 0)
Explain what happened.

2. Try the following sequence:

syms x h
f = exp(sin(x))
m = (subs(f, x+h)-f)/h
f1 = limit(m, h, 0)
subs(f1, pi)
X = -10:.05:10; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Makes an array of x values.

F = subs(f, X); . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Makes an array of f(x) values.

F1 = subs(f1, X);
plot(X, F, b, X, F1, r)
Explain what happened.

3. Now repeat the steps above for the function:

Is the function defined for all real numbers? What about the derivative? How is the graph misleading?

4. Next repeat this procedure for the function.

Are the function and its derivative defined for all real numbers? How is this graph misleading?

5. Use ezplot(f) and ezplot(f1) to get another picture for f and f from #4. In what ways are these graphs misleading?

6. Prepare a brief (< 1>

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