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Unformatted text preview: 3 + a, a2 , x = 3
x = 3. 4. For the given function, (i) sketch by hand f (x) on the interval x ∈ [−2, 2], and (ii) evaluate the
limits limx→0 f (x) and limx→1 f (x), if they exist.
f ( x) = | x + 1| , x
+ x, 0 < x ≤ 1 3 − x, x > 1. 5. Use MATLAB to plot the functions sin x and cos x, on the interval x ∈ [−2π , 2π ]. On the same
graph, plot the function below for h = .5 and h = .05. What can you infer from your plots about
the function as h → 0?
sin(x + h) − sin(x)
6. Determine a value of the constant, a, for which the following limit exists. Find the limit for that
value of a.
3(x2 + 1) + a(x + 1)
x2 + x − 2
7. Determine the limit of the given function, and use the formal deﬁnition to prove your limit
2x 2 − 5x − 3
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- Fall '13