Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 6, Problem 21PE
To determine
To find:The area above the given curve
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A graph of the function f is given below:
Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1
Of is defined at a.
If is not defined at x = a.
Of is continuous at x = a.
If is discontinuous at x = a.
Of is smooth at x = a.
Of is not smooth at = a.
If has a horizontal tangent line at = a.
f has a vertical tangent line at x = a.
Of has a oblique/slanted tangent line at x = a.
If has no tangent line at x = a.
f(a + h) - f(a)
lim
is finite.
h→0
h
f(a + h) - f(a)
lim
h->0+
and lim
h
h->0-
f(a + h) - f(a)
h
are infinite.
lim
does not exist.
h→0
f(a+h) - f(a)
h
f'(a) is defined.
f'(a) is undefined.
If is differentiable at x = a.
If is not differentiable at x = a.
The graph below is the function f(z)
4
3
-2
-1
-1
1
2
3
-3
Consider the function f whose graph is given above.
(A) Find the following. If a function value is undefined, enter "undefined". If a limit does not exist, enter
"DNE". If a limit can be represented by -∞o or ∞o, then do so.
lim f(z)
+3
lim f(z)
1-1
lim f(z)
f(1)
= 2
=
-4
= undefined
lim f(z) 1
2-1
lim f(z):
2-1+
lim f(x)
2+1
-00
= -2
= DNE
f(-1) = -2
lim f(z) = -2
1-4
lim f(z)
2-4°
00
f'(0)
f'(2)
=
=
(B) List the value(s) of x for which f(x) is discontinuous. Then list the value(s) of x for which f(x) is left-
continuous or right-continuous. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5). If
there are none, enter "none".
Discontinuous at z =
Left-continuous at x =
Invalid use of a comma.syntax incomplete.
Right-continuous at z =
Invalid use of a comma.syntax incomplete.
(C) List the value(s) of x for which f(x) is non-differentiable. Enter your answer as a comma-separated list,
if needed (eg. -2, 3, 5).…
A graph of the function f is given below:
Study the graph of f at the value given below. Select each of the following that applies for the value
a = -4.
f is defined at = a.
f is not defined at 2 = a.
If is continuous at x = a.
Of is discontinuous at x = a.
Of is smooth at x = a.
f is not smooth at x = a.
If has a horizontal tangent line at x = a.
f has a vertical tangent line at x = a.
Of has a oblique/slanted tangent line at x = a.
Of has no tangent line at x = a.
f(a + h) − f(a)
h
lim
is finite.
h→0
f(a + h) - f(a)
lim
is infinite.
h→0
h
f(a + h) - f(a)
lim
does not exist.
h→0
h
f'(a) is defined.
f'(a) is undefined.
If is differentiable at x = a.
If is not differentiable at x = a.
Chapter 6 Solutions
Calculus
Ch. 6.1 - Prob. 1PSCh. 6.1 - Prob. 2PSCh. 6.1 - Prob. 3PSCh. 6.1 - Prob. 4PSCh. 6.1 - Prob. 5PSCh. 6.1 - Prob. 6PSCh. 6.1 - Prob. 7PSCh. 6.1 - Prob. 8PSCh. 6.1 - Prob. 9PSCh. 6.1 - Prob. 10PS
Ch. 6.1 - Prob. 11PSCh. 6.1 - Prob. 12PSCh. 6.1 - Prob. 13PSCh. 6.1 - Prob. 14PSCh. 6.1 - Prob. 15PSCh. 6.1 - Prob. 16PSCh. 6.1 - Prob. 17PSCh. 6.1 - Prob. 18PSCh. 6.1 - Prob. 19PSCh. 6.1 - Prob. 20PSCh. 6.1 - Prob. 21PSCh. 6.1 - Prob. 22PSCh. 6.1 - Prob. 23PSCh. 6.1 - Prob. 24PSCh. 6.1 - Prob. 25PSCh. 6.1 - Prob. 26PSCh. 6.1 - Prob. 27PSCh. 6.1 - Prob. 28PSCh. 6.1 - Prob. 29PSCh. 6.1 - Prob. 30PSCh. 6.1 - Prob. 31PSCh. 6.1 - Prob. 32PSCh. 6.1 - Prob. 33PSCh. 6.1 - Prob. 34PSCh. 6.1 - Prob. 35PSCh. 6.1 - Prob. 36PSCh. 6.1 - Prob. 37PSCh. 6.1 - Prob. 38PSCh. 6.1 - Prob. 39PSCh. 6.1 - Prob. 40PSCh. 6.1 - Prob. 41PSCh. 6.1 - Prob. 42PSCh. 6.1 - Prob. 43PSCh. 6.1 - Prob. 44PSCh. 6.1 - Prob. 45PSCh. 6.1 - Prob. 46PSCh. 6.1 - Prob. 47PSCh. 6.1 - Prob. 48PSCh. 6.1 - Prob. 49PSCh. 6.1 - Prob. 50PSCh. 6.1 - Prob. 51PSCh. 6.1 - Prob. 52PSCh. 6.1 - Prob. 53PSCh. 6.1 - Prob. 54PSCh. 6.1 - Prob. 55PSCh. 6.1 - Prob. 56PSCh. 6.1 - Prob. 57PSCh. 6.1 - Prob. 58PSCh. 6.1 - Prob. 59PSCh. 6.1 - Prob. 60PSCh. 6.2 - Prob. 1PSCh. 6.2 - Prob. 2PSCh. 6.2 - Prob. 3PSCh. 6.2 - Prob. 4PSCh. 6.2 - Prob. 5PSCh. 6.2 - Prob. 6PSCh. 6.2 - Prob. 7PSCh. 6.2 - Prob. 8PSCh. 6.2 - Prob. 9PSCh. 6.2 - Prob. 10PSCh. 6.2 - Prob. 11PSCh. 6.2 - Prob. 12PSCh. 6.2 - Prob. 13PSCh. 6.2 - Prob. 14PSCh. 6.2 - Prob. 15PSCh. 6.2 - Prob. 16PSCh. 6.2 - Prob. 17PSCh. 6.2 - Prob. 18PSCh. 6.2 - Prob. 19PSCh. 6.2 - Prob. 20PSCh. 6.2 - Prob. 21PSCh. 6.2 - Prob. 22PSCh. 6.2 - Prob. 23PSCh. 6.2 - Prob. 24PSCh. 6.2 - Prob. 25PSCh. 6.2 - Prob. 26PSCh. 6.2 - Prob. 27PSCh. 6.2 - Prob. 28PSCh. 6.2 - Prob. 29PSCh. 6.2 - Prob. 30PSCh. 6.2 - Prob. 31PSCh. 6.2 - Prob. 32PSCh. 6.2 - Prob. 33PSCh. 6.2 - Prob. 34PSCh. 6.2 - Prob. 35PSCh. 6.2 - Prob. 36PSCh. 6.2 - Prob. 37PSCh. 6.2 - Prob. 38PSCh. 6.2 - Prob. 39PSCh. 6.2 - Prob. 40PSCh. 6.2 - Prob. 41PSCh. 6.2 - Prob. 42PSCh. 6.2 - Prob. 43PSCh. 6.2 - Prob. 44PSCh. 6.2 - Prob. 45PSCh. 6.2 - Prob. 46PSCh. 6.2 - Prob. 47PSCh. 6.2 - Prob. 48PSCh. 6.2 - Prob. 49PSCh. 6.2 - Prob. 50PSCh. 6.2 - Prob. 51PSCh. 6.2 - Prob. 52PSCh. 6.2 - Prob. 53PSCh. 6.2 - Prob. 54PSCh. 6.2 - Prob. 55PSCh. 6.2 - Prob. 56PSCh. 6.2 - Prob. 57PSCh. 6.2 - Prob. 58PSCh. 6.2 - Prob. 59PSCh. 6.2 - Prob. 60PSCh. 6.3 - Prob. 1PSCh. 6.3 - Prob. 2PSCh. 6.3 - Prob. 3PSCh. 6.3 - Prob. 4PSCh. 6.3 - Prob. 5PSCh. 6.3 - Prob. 6PSCh. 6.3 - Prob. 7PSCh. 6.3 - Prob. 8PSCh. 6.3 - Prob. 9PSCh. 6.3 - Prob. 10PSCh. 6.3 - Prob. 11PSCh. 6.3 - Prob. 12PSCh. 6.3 - Prob. 13PSCh. 6.3 - Prob. 14PSCh. 6.3 - Prob. 15PSCh. 6.3 - Prob. 16PSCh. 6.3 - Prob. 17PSCh. 6.3 - Prob. 18PSCh. 6.3 - Prob. 19PSCh. 6.3 - Prob. 20PSCh. 6.3 - Prob. 21PSCh. 6.3 - Prob. 22PSCh. 6.3 - Prob. 23PSCh. 6.3 - Prob. 24PSCh. 6.3 - Prob. 25PSCh. 6.3 - Prob. 26PSCh. 6.3 - Prob. 27PSCh. 6.3 - Prob. 28PSCh. 6.3 - Prob. 29PSCh. 6.3 - Prob. 30PSCh. 6.3 - Prob. 31PSCh. 6.3 - Prob. 32PSCh. 6.3 - Prob. 33PSCh. 6.3 - Prob. 34PSCh. 6.3 - Prob. 35PSCh. 6.3 - Prob. 36PSCh. 6.3 - Prob. 37PSCh. 6.3 - Prob. 38PSCh. 6.3 - Prob. 39PSCh. 6.3 - Prob. 40PSCh. 6.3 - Prob. 41PSCh. 6.3 - Prob. 42PSCh. 6.3 - Prob. 43PSCh. 6.3 - Prob. 44PSCh. 6.3 - Prob. 45PSCh. 6.3 - Prob. 46PSCh. 6.3 - Prob. 47PSCh. 6.3 - Prob. 48PSCh. 6.3 - Prob. 49PSCh. 6.3 - Prob. 50PSCh. 6.3 - Prob. 51PSCh. 6.3 - Prob. 52PSCh. 6.3 - Prob. 53PSCh. 6.3 - Prob. 54PSCh. 6.3 - Prob. 55PSCh. 6.3 - Prob. 56PSCh. 6.3 - Prob. 57PSCh. 6.3 - Prob. 58PSCh. 6.3 - Prob. 59PSCh. 6.3 - Prob. 60PSCh. 6.4 - Prob. 1PSCh. 6.4 - Prob. 2PSCh. 6.4 - Prob. 3PSCh. 6.4 - Prob. 4PSCh. 6.4 - Prob. 5PSCh. 6.4 - Prob. 6PSCh. 6.4 - Prob. 7PSCh. 6.4 - Prob. 8PSCh. 6.4 - Prob. 9PSCh. 6.4 - Prob. 10PSCh. 6.4 - Prob. 11PSCh. 6.4 - Prob. 12PSCh. 6.4 - Prob. 13PSCh. 6.4 - Prob. 14PSCh. 6.4 - Prob. 15PSCh. 6.4 - Prob. 16PSCh. 6.4 - Prob. 17PSCh. 6.4 - Prob. 18PSCh. 6.4 - Prob. 19PSCh. 6.4 - Prob. 20PSCh. 6.4 - Prob. 21PSCh. 6.4 - Prob. 22PSCh. 6.4 - Prob. 23PSCh. 6.4 - Prob. 24PSCh. 6.4 - Prob. 25PSCh. 6.4 - Prob. 26PSCh. 6.4 - Prob. 27PSCh. 6.4 - Prob. 28PSCh. 6.4 - Prob. 29PSCh. 6.4 - Prob. 30PSCh. 6.4 - Prob. 31PSCh. 6.4 - Prob. 32PSCh. 6.4 - Prob. 33PSCh. 6.4 - Prob. 34PSCh. 6.4 - Prob. 35PSCh. 6.4 - Prob. 36PSCh. 6.4 - Prob. 37PSCh. 6.4 - Prob. 38PSCh. 6.4 - Prob. 39PSCh. 6.4 - Prob. 40PSCh. 6.4 - Prob. 41PSCh. 6.4 - Prob. 42PSCh. 6.4 - Prob. 43PSCh. 6.4 - Prob. 44PSCh. 6.4 - Prob. 45PSCh. 6.4 - Prob. 46PSCh. 6.4 - Prob. 47PSCh. 6.4 - Prob. 48PSCh. 6.4 - Prob. 49PSCh. 6.4 - Prob. 50PSCh. 6.4 - Prob. 51PSCh. 6.4 - Prob. 52PSCh. 6.4 - Prob. 53PSCh. 6.4 - Prob. 54PSCh. 6.4 - Prob. 55PSCh. 6.4 - Prob. 56PSCh. 6.4 - Prob. 57PSCh. 6.4 - Prob. 58PSCh. 6.4 - Prob. 59PSCh. 6.4 - Prob. 60PSCh. 6.5 - Prob. 1PSCh. 6.5 - Prob. 2PSCh. 6.5 - Prob. 3PSCh. 6.5 - Prob. 4PSCh. 6.5 - Prob. 5PSCh. 6.5 - Prob. 6PSCh. 6.5 - Prob. 7PSCh. 6.5 - Prob. 8PSCh. 6.5 - Prob. 9PSCh. 6.5 - Prob. 10PSCh. 6.5 - Prob. 11PSCh. 6.5 - Prob. 12PSCh. 6.5 - Prob. 13PSCh. 6.5 - Prob. 14PSCh. 6.5 - Prob. 15PSCh. 6.5 - Prob. 16PSCh. 6.5 - Prob. 17PSCh. 6.5 - Prob. 18PSCh. 6.5 - Prob. 19PSCh. 6.5 - Prob. 20PSCh. 6.5 - Prob. 21PSCh. 6.5 - Prob. 22PSCh. 6.5 - Prob. 23PSCh. 6.5 - Prob. 24PSCh. 6.5 - Prob. 25PSCh. 6.5 - Prob. 26PSCh. 6.5 - Prob. 27PSCh. 6.5 - Prob. 28PSCh. 6.5 - Prob. 29PSCh. 6.5 - Prob. 30PSCh. 6.5 - Prob. 31PSCh. 6.5 - Prob. 32PSCh. 6.5 - Prob. 33PSCh. 6.5 - Prob. 34PSCh. 6.5 - Prob. 35PSCh. 6.5 - Prob. 36PSCh. 6.5 - Prob. 37PSCh. 6.5 - Prob. 38PSCh. 6.5 - Prob. 39PSCh. 6.5 - Prob. 40PSCh. 6.5 - Prob. 41PSCh. 6.5 - Prob. 42PSCh. 6.5 - Prob. 43PSCh. 6.5 - Prob. 44PSCh. 6.5 - Prob. 45PSCh. 6.5 - Prob. 46PSCh. 6.5 - Prob. 47PSCh. 6.5 - Prob. 48PSCh. 6.5 - Prob. 49PSCh. 6.5 - Prob. 50PSCh. 6.5 - Prob. 51PSCh. 6.5 - Prob. 52PSCh. 6.5 - Prob. 53PSCh. 6.5 - Prob. 54PSCh. 6.5 - Prob. 55PSCh. 6.5 - Prob. 56PSCh. 6.5 - Prob. 57PSCh. 6.5 - Prob. 58PSCh. 6.5 - Prob. 59PSCh. 6.5 - Prob. 60PSCh. 6.6 - Prob. 1PSCh. 6.6 - Prob. 2PSCh. 6.6 - Prob. 3PSCh. 6.6 - Prob. 4PSCh. 6.6 - Prob. 5PSCh. 6.6 - Prob. 6PSCh. 6.6 - Prob. 7PSCh. 6.6 - Prob. 8PSCh. 6.6 - Prob. 9PSCh. 6.6 - Prob. 10PSCh. 6.6 - Prob. 11PSCh. 6.6 - Prob. 12PSCh. 6.6 - Prob. 13PSCh. 6.6 - Prob. 14PSCh. 6.6 - Prob. 15PSCh. 6.6 - Prob. 16PSCh. 6.6 - Prob. 17PSCh. 6.6 - Prob. 18PSCh. 6.6 - Prob. 19PSCh. 6.6 - Prob. 20PSCh. 6.6 - Prob. 21PSCh. 6.6 - Prob. 22PSCh. 6.6 - Prob. 23PSCh. 6.6 - Prob. 24PSCh. 6.6 - Prob. 25PSCh. 6.6 - Prob. 26PSCh. 6.6 - Prob. 27PSCh. 6.6 - Prob. 28PSCh. 6.6 - Prob. 29PSCh. 6.6 - Prob. 30PSCh. 6.6 - Prob. 31PSCh. 6.6 - Prob. 32PSCh. 6.6 - Prob. 33PSCh. 6.6 - Prob. 34PSCh. 6.6 - Prob. 35PSCh. 6.6 - Prob. 36PSCh. 6.6 - Prob. 37PSCh. 6.6 - Prob. 38PSCh. 6.6 - Prob. 39PSCh. 6.6 - Prob. 40PSCh. 6.6 - Prob. 41PSCh. 6.6 - Prob. 42PSCh. 6.6 - Prob. 43PSCh. 6.6 - Prob. 44PSCh. 6.6 - Prob. 45PSCh. 6.6 - Prob. 46PSCh. 6.6 - Prob. 47PSCh. 6.6 - Prob. 48PSCh. 6.6 - Prob. 49PSCh. 6.6 - Prob. 50PSCh. 6.6 - Prob. 51PSCh. 6.6 - Prob. 52PSCh. 6.6 - Prob. 53PSCh. 6.6 - Prob. 54PSCh. 6.6 - Prob. 55PSCh. 6.6 - Prob. 56PSCh. 6.6 - Prob. 57PSCh. 6.6 - Prob. 58PSCh. 6.6 - Prob. 59PSCh. 6.6 - Prob. 60PSCh. 6 - Prob. 1PECh. 6 - Prob. 2PECh. 6 - Prob. 3PECh. 6 - Prob. 4PECh. 6 - Prob. 5PECh. 6 - Prob. 6PECh. 6 - Prob. 7PECh. 6 - Prob. 8PECh. 6 - Prob. 9PECh. 6 - Prob. 10PECh. 6 - Prob. 11PECh. 6 - Prob. 12PECh. 6 - Prob. 13PECh. 6 - Prob. 14PECh. 6 - Prob. 15PECh. 6 - Prob. 16PECh. 6 - Prob. 17PECh. 6 - Prob. 18PECh. 6 - Prob. 19PECh. 6 - Prob. 20PECh. 6 - Prob. 21PECh. 6 - Prob. 22PECh. 6 - Prob. 23PECh. 6 - Prob. 24PECh. 6 - Prob. 25PECh. 6 - Prob. 26PECh. 6 - Prob. 27PECh. 6 - Prob. 28PECh. 6 - Prob. 29PECh. 6 - Prob. 30PECh. 6 - Prob. 1SPCh. 6 - Prob. 2SPCh. 6 - Prob. 3SPCh. 6 - Prob. 4SPCh. 6 - Prob. 5SPCh. 6 - Prob. 6SPCh. 6 - Prob. 7SPCh. 6 - Prob. 8SPCh. 6 - Prob. 9SPCh. 6 - Prob. 10SPCh. 6 - Prob. 11SPCh. 6 - Prob. 12SPCh. 6 - Prob. 13SPCh. 6 - Prob. 14SPCh. 6 - Prob. 15SPCh. 6 - Prob. 16SPCh. 6 - Prob. 17SPCh. 6 - Prob. 18SPCh. 6 - Prob. 19SPCh. 6 - Prob. 20SPCh. 6 - Prob. 21SPCh. 6 - Prob. 22SPCh. 6 - Prob. 23SPCh. 6 - Prob. 24SPCh. 6 - Prob. 25SPCh. 6 - Prob. 26SPCh. 6 - Prob. 27SPCh. 6 - Prob. 28SPCh. 6 - Prob. 29SPCh. 6 - Prob. 30SPCh. 6 - Prob. 31SPCh. 6 - Prob. 32SPCh. 6 - Prob. 33SPCh. 6 - Prob. 34SPCh. 6 - Prob. 35SPCh. 6 - Prob. 36SPCh. 6 - Prob. 37SPCh. 6 - Prob. 38SPCh. 6 - Prob. 39SPCh. 6 - Prob. 40SPCh. 6 - Prob. 41SPCh. 6 - Prob. 42SPCh. 6 - Prob. 43SPCh. 6 - Prob. 44SPCh. 6 - Prob. 45SPCh. 6 - Prob. 46SPCh. 6 - Prob. 47SPCh. 6 - Prob. 48SPCh. 6 - Prob. 49SPCh. 6 - Prob. 50SPCh. 6 - Prob. 51SPCh. 6 - Prob. 52SPCh. 6 - Prob. 53SPCh. 6 - Prob. 54SPCh. 6 - Prob. 55SPCh. 6 - Prob. 56SPCh. 6 - Prob. 57SPCh. 6 - Prob. 58SPCh. 6 - Prob. 59SPCh. 6 - Prob. 60SPCh. 6 - Prob. 61SPCh. 6 - Prob. 62SPCh. 6 - Prob. 63SPCh. 6 - Prob. 64SPCh. 6 - Prob. 65SPCh. 6 - Prob. 66SPCh. 6 - Prob. 67SPCh. 6 - Prob. 68SPCh. 6 - Prob. 69SPCh. 6 - Prob. 70SPCh. 6 - Prob. 71SPCh. 6 - Prob. 72SPCh. 6 - Prob. 73SPCh. 6 - Prob. 74SPCh. 6 - Prob. 75SPCh. 6 - Prob. 76SPCh. 6 - Prob. 77SPCh. 6 - Prob. 78SPCh. 6 - Prob. 79SPCh. 6 - Prob. 80SPCh. 6 - Prob. 81SPCh. 6 - Prob. 82SPCh. 6 - Prob. 83SPCh. 6 - Prob. 84SPCh. 6 - Prob. 85SPCh. 6 - Prob. 86SPCh. 6 - Prob. 87SPCh. 6 - Prob. 88SPCh. 6 - Prob. 89SPCh. 6 - Prob. 90SPCh. 6 - Prob. 91SPCh. 6 - Prob. 92SPCh. 6 - Prob. 93SPCh. 6 - Prob. 94SPCh. 6 - Prob. 95SPCh. 6 - Prob. 96SPCh. 6 - Prob. 97SPCh. 6 - Prob. 98SPCh. 6 - Prob. 99SP
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