Student's Solution and Survival Manual for Calculus
7th Edition
ISBN: 9781524934040
Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J
Publisher: Kendall Hunt Publishing
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Chapter 4.2, Problem 38PS
To determine
To prove:
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Prove this theorem
The Fundamental Theorem of Calculus, Part 1:
If f is continuous on [a,b], then the function g defined
by
g(x)%3D S" f (t) dt, a < x < b
is continuous on [a,b], and differentiable on (a,b), and
d (x) = f (x).
Consider the function f(x)
1
on the interval [- 4, 4).
a. Is f(-4) = f(4)?
Yes No
b. Is f continuous on [- 4, 4]?
Yes No
c. Is f differentiable on (- 4, 4)?
Yes No
d. What do your answers to parts a., b., and c. imply?
O Rolle's Theorem can be applied
The Mean Value Theorem can be applied
O Both Rolle's Theorem and the Mena Value Theorem can be applied
O Neither Rolle's Theorem nor the Mean Value Theorem applies to this problem
e. If you can use Rolle's Theorem or the Mean Value Theorem, find the value of c satisfying said
theorem. If not, enter DNE. Answers should be in exact form (i.e., do not use a calculator to get a
decimal approximation).
c =
4.
5n
6.
Chapter 4 Solutions
Student's Solution and Survival Manual for Calculus
Ch. 4.1 - Prob. 1PSCh. 4.1 - Prob. 2PSCh. 4.1 - Prob. 3PSCh. 4.1 - Prob. 4PSCh. 4.1 - Prob. 5PSCh. 4.1 - Prob. 6PSCh. 4.1 - Prob. 7PSCh. 4.1 - Prob. 8PSCh. 4.1 - Prob. 9PSCh. 4.1 - Prob. 10PS
Ch. 4.1 - Prob. 11PSCh. 4.1 - Prob. 12PSCh. 4.1 - Prob. 13PSCh. 4.1 - Prob. 14PSCh. 4.1 - Prob. 15PSCh. 4.1 - Prob. 16PSCh. 4.1 - Prob. 17PSCh. 4.1 - Prob. 18PSCh. 4.1 - Prob. 19PSCh. 4.1 - Prob. 20PSCh. 4.1 - Prob. 21PSCh. 4.1 - Prob. 22PSCh. 4.1 - Prob. 23PSCh. 4.1 - Prob. 24PSCh. 4.1 - Prob. 25PSCh. 4.1 - Prob. 26PSCh. 4.1 - Prob. 27PSCh. 4.1 - Prob. 28PSCh. 4.1 - Prob. 29PSCh. 4.1 - Prob. 30PSCh. 4.1 - Prob. 31PSCh. 4.1 - Prob. 32PSCh. 4.1 - Prob. 33PSCh. 4.1 - Prob. 34PSCh. 4.1 - Prob. 35PSCh. 4.1 - Prob. 36PSCh. 4.1 - Prob. 37PSCh. 4.1 - Prob. 38PSCh. 4.1 - Prob. 39PSCh. 4.1 - Prob. 40PSCh. 4.1 - Prob. 41PSCh. 4.1 - Prob. 42PSCh. 4.1 - Prob. 43PSCh. 4.1 - Prob. 44PSCh. 4.1 - Prob. 45PSCh. 4.1 - Prob. 46PSCh. 4.1 - Prob. 47PSCh. 4.1 - Prob. 48PSCh. 4.1 - Prob. 49PSCh. 4.1 - Prob. 50PSCh. 4.1 - Prob. 51PSCh. 4.1 - Prob. 52PSCh. 4.1 - Prob. 53PSCh. 4.1 - Prob. 54PSCh. 4.1 - Prob. 55PSCh. 4.1 - Prob. 56PSCh. 4.1 - Prob. 57PSCh. 4.1 - Prob. 58PSCh. 4.1 - Prob. 59PSCh. 4.1 - Prob. 60PSCh. 4.2 - Prob. 1PSCh. 4.2 - Prob. 2PSCh. 4.2 - Prob. 3PSCh. 4.2 - Prob. 4PSCh. 4.2 - Prob. 5PSCh. 4.2 - Prob. 6PSCh. 4.2 - Prob. 7PSCh. 4.2 - Prob. 8PSCh. 4.2 - Prob. 9PSCh. 4.2 - Prob. 10PSCh. 4.2 - Prob. 11PSCh. 4.2 - Prob. 12PSCh. 4.2 - Prob. 13PSCh. 4.2 - Prob. 14PSCh. 4.2 - Prob. 15PSCh. 4.2 - Prob. 16PSCh. 4.2 - Prob. 17PSCh. 4.2 - Prob. 18PSCh. 4.2 - Prob. 19PSCh. 4.2 - Prob. 20PSCh. 4.2 - Prob. 21PSCh. 4.2 - Prob. 22PSCh. 4.2 - Prob. 23PSCh. 4.2 - Prob. 24PSCh. 4.2 - Prob. 25PSCh. 4.2 - Prob. 26PSCh. 4.2 - Prob. 27PSCh. 4.2 - Prob. 28PSCh. 4.2 - Prob. 29PSCh. 4.2 - Prob. 30PSCh. 4.2 - Prob. 31PSCh. 4.2 - Prob. 32PSCh. 4.2 - Prob. 33PSCh. 4.2 - Prob. 34PSCh. 4.2 - Prob. 35PSCh. 4.2 - Prob. 36PSCh. 4.2 - Prob. 37PSCh. 4.2 - Prob. 38PSCh. 4.2 - Prob. 39PSCh. 4.2 - Prob. 40PSCh. 4.2 - Prob. 41PSCh. 4.2 - Prob. 42PSCh. 4.2 - Prob. 43PSCh. 4.2 - Prob. 44PSCh. 4.2 - Prob. 45PSCh. 4.2 - Prob. 46PSCh. 4.2 - Prob. 47PSCh. 4.2 - Prob. 48PSCh. 4.2 - Prob. 49PSCh. 4.2 - Prob. 50PSCh. 4.2 - Prob. 51PSCh. 4.2 - Prob. 52PSCh. 4.2 - Prob. 53PSCh. 4.2 - Prob. 54PSCh. 4.2 - Prob. 55PSCh. 4.2 - Prob. 56PSCh. 4.2 - Prob. 57PSCh. 4.2 - Prob. 58PSCh. 4.2 - Prob. 59PSCh. 4.2 - Prob. 60PSCh. 4.3 - Prob. 1PSCh. 4.3 - Prob. 2PSCh. 4.3 - Prob. 3PSCh. 4.3 - Prob. 4PSCh. 4.3 - Prob. 5PSCh. 4.3 - Prob. 6PSCh. 4.3 - Prob. 7PSCh. 4.3 - Prob. 8PSCh. 4.3 - Prob. 9PSCh. 4.3 - Prob. 10PSCh. 4.3 - Prob. 11PSCh. 4.3 - Prob. 12PSCh. 4.3 - Prob. 13PSCh. 4.3 - Prob. 14PSCh. 4.3 - Prob. 15PSCh. 4.3 - Prob. 16PSCh. 4.3 - Prob. 17PSCh. 4.3 - Prob. 18PSCh. 4.3 - Prob. 19PSCh. 4.3 - Prob. 20PSCh. 4.3 - Prob. 21PSCh. 4.3 - Prob. 22PSCh. 4.3 - Prob. 23PSCh. 4.3 - Prob. 24PSCh. 4.3 - Prob. 25PSCh. 4.3 - Prob. 26PSCh. 4.3 - Prob. 27PSCh. 4.3 - Prob. 28PSCh. 4.3 - Prob. 29PSCh. 4.3 - Prob. 30PSCh. 4.3 - Prob. 31PSCh. 4.3 - Prob. 32PSCh. 4.3 - Prob. 33PSCh. 4.3 - Prob. 34PSCh. 4.3 - Prob. 35PSCh. 4.3 - Prob. 36PSCh. 4.3 - Prob. 37PSCh. 4.3 - Prob. 38PSCh. 4.3 - Prob. 39PSCh. 4.3 - Prob. 40PSCh. 4.3 - Prob. 41PSCh. 4.3 - Prob. 42PSCh. 4.3 - Prob. 43PSCh. 4.3 - Prob. 44PSCh. 4.3 - Prob. 45PSCh. 4.3 - Prob. 46PSCh. 4.3 - Prob. 47PSCh. 4.3 - Prob. 48PSCh. 4.3 - Prob. 49PSCh. 4.3 - Prob. 50PSCh. 4.3 - Prob. 51PSCh. 4.3 - Prob. 52PSCh. 4.3 - Prob. 53PSCh. 4.3 - Prob. 54PSCh. 4.3 - Prob. 55PSCh. 4.3 - Prob. 56PSCh. 4.3 - Prob. 57PSCh. 4.3 - Prob. 58PSCh. 4.3 - Prob. 59PSCh. 4.3 - Prob. 60PSCh. 4.4 - Prob. 1PSCh. 4.4 - Prob. 2PSCh. 4.4 - Prob. 3PSCh. 4.4 - Prob. 4PSCh. 4.4 - Prob. 5PSCh. 4.4 - Prob. 6PSCh. 4.4 - Prob. 7PSCh. 4.4 - Prob. 8PSCh. 4.4 - Prob. 9PSCh. 4.4 - Prob. 10PSCh. 4.4 - Prob. 11PSCh. 4.4 - Prob. 12PSCh. 4.4 - Prob. 13PSCh. 4.4 - Prob. 14PSCh. 4.4 - Prob. 15PSCh. 4.4 - Prob. 16PSCh. 4.4 - Prob. 17PSCh. 4.4 - Prob. 18PSCh. 4.4 - Prob. 19PSCh. 4.4 - Prob. 20PSCh. 4.4 - Prob. 21PSCh. 4.4 - Prob. 22PSCh. 4.4 - Prob. 23PSCh. 4.4 - Prob. 24PSCh. 4.4 - Prob. 25PSCh. 4.4 - Prob. 26PSCh. 4.4 - Prob. 27PSCh. 4.4 - Prob. 28PSCh. 4.4 - Prob. 29PSCh. 4.4 - Prob. 30PSCh. 4.4 - Prob. 31PSCh. 4.4 - Prob. 32PSCh. 4.4 - Prob. 33PSCh. 4.4 - Prob. 34PSCh. 4.4 - Prob. 35PSCh. 4.4 - Prob. 36PSCh. 4.4 - Prob. 37PSCh. 4.4 - Prob. 38PSCh. 4.4 - Prob. 39PSCh. 4.4 - Prob. 40PSCh. 4.4 - Prob. 41PSCh. 4.4 - Prob. 42PSCh. 4.4 - Prob. 43PSCh. 4.4 - Prob. 44PSCh. 4.4 - Prob. 45PSCh. 4.4 - Prob. 46PSCh. 4.4 - Prob. 47PSCh. 4.4 - Prob. 48PSCh. 4.4 - Prob. 49PSCh. 4.4 - Prob. 50PSCh. 4.4 - Prob. 51PSCh. 4.4 - Prob. 52PSCh. 4.4 - Prob. 53PSCh. 4.4 - Prob. 54PSCh. 4.4 - Prob. 55PSCh. 4.4 - Prob. 56PSCh. 4.4 - Prob. 57PSCh. 4.4 - Prob. 58PSCh. 4.4 - Prob. 59PSCh. 4.4 - Prob. 60PSCh. 4.5 - Prob. 1PSCh. 4.5 - Prob. 2PSCh. 4.5 - Prob. 3PSCh. 4.5 - Prob. 4PSCh. 4.5 - Prob. 5PSCh. 4.5 - Prob. 6PSCh. 4.5 - Prob. 7PSCh. 4.5 - Prob. 8PSCh. 4.5 - Prob. 9PSCh. 4.5 - Prob. 10PSCh. 4.5 - Prob. 11PSCh. 4.5 - Prob. 12PSCh. 4.5 - Prob. 13PSCh. 4.5 - Prob. 14PSCh. 4.5 - Prob. 15PSCh. 4.5 - Prob. 16PSCh. 4.5 - Prob. 17PSCh. 4.5 - Prob. 18PSCh. 4.5 - Prob. 19PSCh. 4.5 - Prob. 20PSCh. 4.5 - Prob. 21PSCh. 4.5 - Prob. 22PSCh. 4.5 - Prob. 23PSCh. 4.5 - Prob. 24PSCh. 4.5 - Prob. 25PSCh. 4.5 - Prob. 26PSCh. 4.5 - Prob. 27PSCh. 4.5 - Prob. 28PSCh. 4.5 - Prob. 29PSCh. 4.5 - Prob. 30PSCh. 4.5 - Prob. 31PSCh. 4.5 - Prob. 32PSCh. 4.5 - Prob. 33PSCh. 4.5 - Prob. 34PSCh. 4.5 - Prob. 35PSCh. 4.5 - Prob. 36PSCh. 4.5 - Prob. 37PSCh. 4.5 - Prob. 38PSCh. 4.5 - Prob. 39PSCh. 4.5 - Prob. 40PSCh. 4.5 - Prob. 41PSCh. 4.5 - Prob. 42PSCh. 4.5 - Prob. 43PSCh. 4.5 - Prob. 44PSCh. 4.5 - Prob. 45PSCh. 4.5 - Prob. 46PSCh. 4.5 - Prob. 47PSCh. 4.5 - Prob. 48PSCh. 4.5 - Prob. 49PSCh. 4.5 - Prob. 50PSCh. 4.5 - Prob. 51PSCh. 4.5 - Prob. 52PSCh. 4.5 - Prob. 53PSCh. 4.5 - Prob. 54PSCh. 4.5 - Prob. 55PSCh. 4.5 - Prob. 56PSCh. 4.5 - Prob. 57PSCh. 4.5 - Prob. 58PSCh. 4.5 - Prob. 59PSCh. 4.5 - Prob. 60PSCh. 4.6 - Prob. 1PSCh. 4.6 - Prob. 2PSCh. 4.6 - Prob. 3PSCh. 4.6 - Prob. 4PSCh. 4.6 - Prob. 5PSCh. 4.6 - Prob. 6PSCh. 4.6 - Prob. 7PSCh. 4.6 - Prob. 8PSCh. 4.6 - Prob. 9PSCh. 4.6 - Prob. 10PSCh. 4.6 - Prob. 11PSCh. 4.6 - Prob. 12PSCh. 4.6 - Prob. 13PSCh. 4.6 - Prob. 14PSCh. 4.6 - Prob. 15PSCh. 4.6 - Prob. 16PSCh. 4.6 - Prob. 17PSCh. 4.6 - Prob. 18PSCh. 4.6 - Prob. 19PSCh. 4.6 - Prob. 20PSCh. 4.6 - Prob. 21PSCh. 4.6 - Prob. 22PSCh. 4.6 - Prob. 23PSCh. 4.6 - Prob. 24PSCh. 4.6 - Prob. 25PSCh. 4.6 - Prob. 26PSCh. 4.6 - Prob. 27PSCh. 4.6 - Prob. 28PSCh. 4.6 - Prob. 29PSCh. 4.6 - Prob. 30PSCh. 4.6 - Prob. 31PSCh. 4.6 - Prob. 32PSCh. 4.6 - Prob. 33PSCh. 4.6 - Prob. 34PSCh. 4.6 - Prob. 35PSCh. 4.6 - Prob. 36PSCh. 4.6 - Prob. 37PSCh. 4.6 - Prob. 38PSCh. 4.6 - Prob. 39PSCh. 4.6 - Prob. 40PSCh. 4.6 - Prob. 41PSCh. 4.6 - Prob. 42PSCh. 4.6 - Prob. 43PSCh. 4.6 - Prob. 44PSCh. 4.6 - Prob. 45PSCh. 4.6 - Prob. 46PSCh. 4.6 - Prob. 47PSCh. 4.6 - Prob. 48PSCh. 4.6 - Prob. 49PSCh. 4.6 - Prob. 50PSCh. 4.6 - Prob. 51PSCh. 4.6 - Prob. 52PSCh. 4.6 - Prob. 53PSCh. 4.6 - Prob. 54PSCh. 4.6 - Prob. 55PSCh. 4.6 - Prob. 56PSCh. 4.6 - Prob. 57PSCh. 4.6 - Prob. 58PSCh. 4.6 - Prob. 59PSCh. 4.6 - Prob. 60PSCh. 4.7 - Prob. 1PSCh. 4.7 - Prob. 2PSCh. 4.7 - Prob. 3PSCh. 4.7 - Prob. 4PSCh. 4.7 - Prob. 5PSCh. 4.7 - Prob. 6PSCh. 4.7 - Prob. 7PSCh. 4.7 - Prob. 8PSCh. 4.7 - Prob. 9PSCh. 4.7 - Prob. 10PSCh. 4.7 - Prob. 11PSCh. 4.7 - Prob. 12PSCh. 4.7 - Prob. 13PSCh. 4.7 - Prob. 14PSCh. 4.7 - Prob. 15PSCh. 4.7 - Prob. 16PSCh. 4.7 - Prob. 17PSCh. 4.7 - Prob. 18PSCh. 4.7 - Prob. 19PSCh. 4.7 - Prob. 20PSCh. 4.7 - Prob. 21PSCh. 4.7 - Prob. 22PSCh. 4.7 - Prob. 23PSCh. 4.7 - Prob. 24PSCh. 4.7 - Prob. 25PSCh. 4.7 - Prob. 26PSCh. 4.7 - Prob. 27PSCh. 4.7 - Prob. 28PSCh. 4.7 - Prob. 29PSCh. 4.7 - Prob. 30PSCh. 4.7 - Prob. 31PSCh. 4.7 - Prob. 32PSCh. 4.7 - Prob. 33PSCh. 4.7 - Prob. 34PSCh. 4.7 - Prob. 35PSCh. 4.7 - Prob. 36PSCh. 4.7 - Prob. 37PSCh. 4.7 - Prob. 38PSCh. 4.7 - Prob. 39PSCh. 4.7 - Prob. 40PSCh. 4.7 - Prob. 41PSCh. 4.7 - Prob. 42PSCh. 4.7 - Prob. 43PSCh. 4.7 - Prob. 44PSCh. 4.7 - Prob. 45PSCh. 4.7 - Prob. 46PSCh. 4.7 - Prob. 47PSCh. 4.7 - Prob. 48PSCh. 4.7 - Prob. 49PSCh. 4.7 - Prob. 50PSCh. 4.7 - Prob. 51PSCh. 4.7 - Prob. 52PSCh. 4.7 - Prob. 53PSCh. 4.7 - Prob. 54PSCh. 4.7 - Prob. 55PSCh. 4.7 - Prob. 56PSCh. 4.7 - Prob. 57PSCh. 4.7 - Prob. 58PSCh. 4.7 - Prob. 59PSCh. 4.7 - Prob. 60PSCh. 4 - Prob. 1PECh. 4 - Prob. 2PECh. 4 - Prob. 3PECh. 4 - Prob. 4PECh. 4 - Prob. 5PECh. 4 - Prob. 6PECh. 4 - Prob. 7PECh. 4 - Prob. 8PECh. 4 - Prob. 9PECh. 4 - Prob. 10PECh. 4 - Prob. 11PECh. 4 - Prob. 12PECh. 4 - Prob. 13PECh. 4 - Prob. 14PECh. 4 - Prob. 15PECh. 4 - Prob. 16PECh. 4 - Prob. 17PECh. 4 - Prob. 18PECh. 4 - Prob. 19PECh. 4 - Prob. 20PECh. 4 - Prob. 21PECh. 4 - Prob. 22PECh. 4 - Prob. 23PECh. 4 - Prob. 24PECh. 4 - Prob. 25PECh. 4 - Prob. 26PECh. 4 - Prob. 27PECh. 4 - Prob. 28PECh. 4 - Prob. 29PECh. 4 - Prob. 30PECh. 4 - Prob. 1SPCh. 4 - Prob. 2SPCh. 4 - Prob. 3SPCh. 4 - Prob. 4SPCh. 4 - Prob. 5SPCh. 4 - Prob. 6SPCh. 4 - Prob. 7SPCh. 4 - Prob. 8SPCh. 4 - Prob. 9SPCh. 4 - Prob. 10SPCh. 4 - Prob. 11SPCh. 4 - Prob. 12SPCh. 4 - Prob. 13SPCh. 4 - Prob. 14SPCh. 4 - Prob. 15SPCh. 4 - Prob. 16SPCh. 4 - Prob. 17SPCh. 4 - Prob. 18SPCh. 4 - Prob. 19SPCh. 4 - Prob. 20SPCh. 4 - Prob. 21SPCh. 4 - Prob. 22SPCh. 4 - Prob. 23SPCh. 4 - Prob. 24SPCh. 4 - Prob. 25SPCh. 4 - Prob. 26SPCh. 4 - Prob. 27SPCh. 4 - Prob. 28SPCh. 4 - Prob. 29SPCh. 4 - Prob. 30SPCh. 4 - Prob. 31SPCh. 4 - Prob. 32SPCh. 4 - Prob. 33SPCh. 4 - Prob. 34SPCh. 4 - Prob. 35SPCh. 4 - Prob. 36SPCh. 4 - Prob. 37SPCh. 4 - Prob. 38SPCh. 4 - Prob. 39SPCh. 4 - Prob. 40SPCh. 4 - Prob. 41SPCh. 4 - Prob. 42SPCh. 4 - Prob. 43SPCh. 4 - Prob. 44SPCh. 4 - Prob. 45SPCh. 4 - Prob. 46SPCh. 4 - Prob. 47SPCh. 4 - Prob. 48SPCh. 4 - Prob. 49SPCh. 4 - Prob. 50SPCh. 4 - Prob. 51SPCh. 4 - Prob. 52SPCh. 4 - Prob. 53SPCh. 4 - Prob. 54SPCh. 4 - Prob. 55SPCh. 4 - Prob. 56SPCh. 4 - Prob. 57SPCh. 4 - Prob. 58SPCh. 4 - Prob. 59SPCh. 4 - Prob. 60SPCh. 4 - Prob. 61SPCh. 4 - Prob. 62SPCh. 4 - Prob. 63SPCh. 4 - Prob. 64SPCh. 4 - Prob. 65SPCh. 4 - Prob. 66SPCh. 4 - Prob. 67SPCh. 4 - Prob. 68SPCh. 4 - Prob. 69SPCh. 4 - Prob. 70SPCh. 4 - Prob. 71SPCh. 4 - Prob. 72SPCh. 4 - Prob. 73SPCh. 4 - Prob. 74SPCh. 4 - Prob. 75SPCh. 4 - Prob. 76SPCh. 4 - Prob. 77SPCh. 4 - Prob. 78SPCh. 4 - Prob. 79SPCh. 4 - Prob. 80SPCh. 4 - Prob. 81SPCh. 4 - Prob. 82SPCh. 4 - Prob. 83SPCh. 4 - Prob. 84SPCh. 4 - Prob. 85SPCh. 4 - Prob. 86SPCh. 4 - Prob. 87SPCh. 4 - Prob. 88SPCh. 4 - Prob. 89SPCh. 4 - Prob. 90SPCh. 4 - Prob. 91SPCh. 4 - Prob. 92SPCh. 4 - Prob. 93SPCh. 4 - Prob. 94SPCh. 4 - Prob. 95SPCh. 4 - Prob. 96SPCh. 4 - Prob. 97SPCh. 4 - Prob. 98SPCh. 4 - Prob. 99SP
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Q1 Theorem 18.1 states that "Let f be a continuous real-valued function on a closed interval [a, b]. Then f is a bounded function.". Read the proof of Theorem 18.1 with [a, b] replaced by (a, b). Where does it break down? Explain.arrow_forwarda) Give an example of a function f : [−2, 3] → R which is not continuous at 1 but which is integrable b) Give an example of a function f : [−2, 2] → R which is not differentiable at −1 but which is continuous at −1 - please include all steps and working with explanationarrow_forwardProve the given theorem and provide (1) examples. Theorem 1.4 (Intermediate Value Theorem) Let f(x) be a continuous in [a, b] and let k be any number between f (a) and f(b). Then there exists a number { in (a, b) such that f({) = k. y=f(x) ¡y=k f(b) f(a) Figure 1.1 Intermediate value theorem.arrow_forward
- Is the proof correct? Either state that it is, or circle the first error and explain what isincorrect about it. If the proof is not correct, can it be fixed to prove the claim true?Claim:If f : (0, 1] → R and g : [1, 2) → R are uniformly continuous on their domains, andf(1) = g(1), then the function h : (0, 2) → R, defined by h(x) = f(x) for x ∈ (0, 1] g(x) for x ∈ [1, 2),is uniformly continuous on (0, 2).Proof:Let e > 0.Since f is uniformly continuous on (0, 1], there exists δ1 > 0 such that if x, y ∈ (0, 1] and|x − y| < δ1, then |f(x) − f(y)| < e/2.Since g is uniformly continuous on [1, 2), there exists δ2 > 0 such that if x, y ∈ [1, 2) and|x − y| < δ2, then |g(x) − g(y)| < e/2.Let δ = min{δ1, δ2}.Now suppose x, y ∈ (0, 2) with x < y and |x − y| < δ.If x, y ∈ (0, 1], then |x − y| < δ ≤ δ1 and so |h(x) − h(y)| = |f(x) − f(y)| < e/2 < e.If x, y ∈ [1, 2), then |x − y| < δ ≤ δ2 and so |h(x) − h(y)| = |g(x) − g(y)| < e/2 < e.If x ∈…arrow_forwardDoes the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = e-2x, [O, 1] O Yes, f is continuous and differentiable on R, so it is continuous on [0, 1] and differentiable on (0, 1). O Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem. O No, f is continuous on [0, 1] but not differentiable on (0, 1). O No, f is not continuous on [0, 1]. O There is not enough information to verify if this function satisfies the Mean Value Theorem. If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).arrow_forward! (asap)arrow_forward
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