Let A := (0, 1] and let f: A R be defined by f(x) = !. Prove that f is continuous on A. Let D := [0, 1] and let f : D→ R be the function defined by f(x) = VT. Show that f is uniformly continuous on D but not Lipschitz there. Determine whether the given function is differentiable at the indicated point(s). (a) h(x) = x|x| at c = 0. (b) k(x) = |r| + |x – 1| at c = 0 and c2 = 1.
Let A := (0, 1] and let f: A R be defined by f(x) = !. Prove that f is continuous on A. Let D := [0, 1] and let f : D→ R be the function defined by f(x) = VT. Show that f is uniformly continuous on D but not Lipschitz there. Determine whether the given function is differentiable at the indicated point(s). (a) h(x) = x|x| at c = 0. (b) k(x) = |r| + |x – 1| at c = 0 and c2 = 1.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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![Let A := (0, 1] and let f: A R be defined by f(x) = !. Prove that f is continuous on A.
Let D := [0, 1] and let f : D→ R be the function defined by f(x) = VT. Show that f is
uniformly continuous on D but not Lipschitz there.
Determine whether the given function is differentiable at the indicated point(s).
(a) h(x) = x|x| at c = 0.
(b) k(x) = |r| + |x – 1| at c = 0 and c2 = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F417549e5-2f85-4501-824f-5e9b4cfcb822%2F5e60f609-1150-421b-a759-128f5f9be925%2Fhnszh07.jpeg&w=3840&q=75)
Transcribed Image Text:Let A := (0, 1] and let f: A R be defined by f(x) = !. Prove that f is continuous on A.
Let D := [0, 1] and let f : D→ R be the function defined by f(x) = VT. Show that f is
uniformly continuous on D but not Lipschitz there.
Determine whether the given function is differentiable at the indicated point(s).
(a) h(x) = x|x| at c = 0.
(b) k(x) = |r| + |x – 1| at c = 0 and c2 = 1.
Expert Solution
Step 1
According to the given information, It is required to prove that:
Step 2
Now, suppose a value of c between (0, 1].
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