Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 7, Problem 71SP
To determine
To calculate : To find length of the arc of the curve
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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.
Find the point of diminishing returns (x,y) for the function R(X), where R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in
thousands of dollars).
R(x) = 10,000-x3 + 42x² + 700x, 0≤x≤20
Chapter 7 Solutions
Calculus
Ch. 7.1 - Prob. 1PSCh. 7.1 - Prob. 2PSCh. 7.1 - Prob. 3PSCh. 7.1 - Prob. 4PSCh. 7.1 - Prob. 5PSCh. 7.1 - Prob. 6PSCh. 7.1 - Prob. 7PSCh. 7.1 - Prob. 8PSCh. 7.1 - Prob. 9PSCh. 7.1 - Prob. 10PS
Ch. 7.1 - Prob. 11PSCh. 7.1 - Prob. 12PSCh. 7.1 - Prob. 13PSCh. 7.1 - Prob. 14PSCh. 7.1 - Prob. 15PSCh. 7.1 - Prob. 16PSCh. 7.1 - Prob. 17PSCh. 7.1 - Prob. 18PSCh. 7.1 - Prob. 19PSCh. 7.1 - Prob. 20PSCh. 7.1 - Prob. 21PSCh. 7.1 - Prob. 22PSCh. 7.1 - Prob. 23PSCh. 7.1 - Prob. 24PSCh. 7.1 - Prob. 25PSCh. 7.1 - Prob. 26PSCh. 7.1 - Prob. 27PSCh. 7.1 - Prob. 28PSCh. 7.1 - Prob. 29PSCh. 7.1 - Prob. 30PSCh. 7.1 - Prob. 31PSCh. 7.1 - Prob. 32PSCh. 7.1 - Prob. 33PSCh. 7.1 - Prob. 34PSCh. 7.1 - Prob. 35PSCh. 7.1 - Prob. 36PSCh. 7.1 - Prob. 37PSCh. 7.1 - Prob. 38PSCh. 7.1 - Prob. 39PSCh. 7.1 - Prob. 40PSCh. 7.1 - Prob. 41PSCh. 7.1 - Prob. 42PSCh. 7.1 - Prob. 43PSCh. 7.1 - Prob. 44PSCh. 7.1 - Prob. 45PSCh. 7.1 - Prob. 46PSCh. 7.1 - Prob. 47PSCh. 7.1 - Prob. 48PSCh. 7.1 - Prob. 49PSCh. 7.1 - Prob. 50PSCh. 7.1 - Prob. 51PSCh. 7.1 - Prob. 52PSCh. 7.1 - Prob. 53PSCh. 7.1 - Prob. 54PSCh. 7.1 - Prob. 55PSCh. 7.1 - Prob. 56PSCh. 7.1 - Prob. 57PSCh. 7.1 - Prob. 58PSCh. 7.1 - Prob. 59PSCh. 7.1 - Prob. 60PSCh. 7.2 - 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Prob. 58PSCh. 7.7 - Prob. 59PSCh. 7.7 - Prob. 60PSCh. 7.8 - Prob. 1PSCh. 7.8 - Prob. 2PSCh. 7.8 - Prob. 3PSCh. 7.8 - Prob. 4PSCh. 7.8 - Prob. 5PSCh. 7.8 - Prob. 6PSCh. 7.8 - Prob. 7PSCh. 7.8 - Prob. 8PSCh. 7.8 - Prob. 9PSCh. 7.8 - Prob. 10PSCh. 7.8 - Prob. 11PSCh. 7.8 - Prob. 12PSCh. 7.8 - Prob. 13PSCh. 7.8 - Prob. 14PSCh. 7.8 - Prob. 15PSCh. 7.8 - Prob. 16PSCh. 7.8 - Prob. 17PSCh. 7.8 - Prob. 18PSCh. 7.8 - Prob. 19PSCh. 7.8 - Prob. 20PSCh. 7.8 - Prob. 21PSCh. 7.8 - Prob. 22PSCh. 7.8 - Prob. 23PSCh. 7.8 - Prob. 24PSCh. 7.8 - Prob. 25PSCh. 7.8 - Prob. 26PSCh. 7.8 - Prob. 27PSCh. 7.8 - Prob. 28PSCh. 7.8 - Prob. 29PSCh. 7.8 - Prob. 30PSCh. 7.8 - Prob. 31PSCh. 7.8 - Prob. 32PSCh. 7.8 - Prob. 33PSCh. 7.8 - Prob. 34PSCh. 7.8 - Prob. 35PSCh. 7.8 - Prob. 36PSCh. 7.8 - Prob. 37PSCh. 7.8 - Prob. 38PSCh. 7.8 - Prob. 39PSCh. 7.8 - Prob. 40PSCh. 7.8 - Prob. 41PSCh. 7.8 - Prob. 42PSCh. 7.8 - Prob. 43PSCh. 7.8 - Prob. 44PSCh. 7.8 - Prob. 45PSCh. 7.8 - Prob. 46PSCh. 7.8 - Prob. 47PSCh. 7.8 - Prob. 48PSCh. 7.8 - 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