111H_hw1 (1)

# 4 for the given function i sketch by hand f x on the

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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| x≤0 + x, 0 &lt; x ≤ 1 3 − x, x &gt; 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) h 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) lim . x→−2 x2 + x − 2 7. Determine the limit of the given function, and use the formal deﬁnition to prove your limit statement. 2x 2 − 5x − 3 lim x→ 3 x−3...
View Full Document

Ask a homework question - tutors are online