APPLIED CALCULUS-WILEYPLUS
6th Edition
ISBN: 9781119267874
Author: Hughes-Hallett
Publisher: WILEY
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Chapter 2.1, Problem 34P
To determine
Estimate the change in y for the given change in x.
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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 2 Solutions
APPLIED CALCULUS-WILEYPLUS
Ch. 2.1 - Prob. 1PCh. 2.1 - Prob. 2PCh. 2.1 - Prob. 3PCh. 2.1 - Prob. 4PCh. 2.1 - Prob. 5PCh. 2.1 - Prob. 6PCh. 2.1 - Prob. 7PCh. 2.1 - Prob. 8PCh. 2.1 - Prob. 9PCh. 2.1 - Prob. 10P
Ch. 2.1 - Prob. 11PCh. 2.1 - Prob. 12PCh. 2.1 - Prob. 13PCh. 2.1 - Prob. 14PCh. 2.1 - Prob. 15PCh. 2.1 - Prob. 16PCh. 2.1 - Prob. 17PCh. 2.1 - Prob. 18PCh. 2.1 - Prob. 19PCh. 2.1 - Prob. 20PCh. 2.1 - Prob. 21PCh. 2.1 - Prob. 22PCh. 2.1 - Prob. 23PCh. 2.1 - Prob. 24PCh. 2.1 - Prob. 25PCh. 2.1 - Prob. 26PCh. 2.1 - Prob. 27PCh. 2.1 - Prob. 28PCh. 2.1 - Prob. 29PCh. 2.1 - Prob. 30PCh. 2.1 - Prob. 31PCh. 2.1 - Prob. 32PCh. 2.1 - Prob. 33PCh. 2.1 - Prob. 34PCh. 2.1 - Prob. 35PCh. 2.1 - Prob. 36PCh. 2.1 - Prob. 37PCh. 2.1 - Prob. 38PCh. 2.1 - Prob. 39PCh. 2.1 - Prob. 40PCh. 2.1 - Prob. 41PCh. 2.2 - Prob. 1PCh. 2.2 - Prob. 2PCh. 2.2 - Prob. 3PCh. 2.2 - Prob. 4PCh. 2.2 - Prob. 5PCh. 2.2 - Prob. 6PCh. 2.2 - Prob. 7PCh. 2.2 - Prob. 8PCh. 2.2 - Prob. 9PCh. 2.2 - Prob. 10PCh. 2.2 - Prob. 11PCh. 2.2 - Prob. 12PCh. 2.2 - Prob. 13PCh. 2.2 - Prob. 14PCh. 2.2 - Prob. 15PCh. 2.2 - Prob. 16PCh. 2.2 - Prob. 17PCh. 2.2 - Prob. 18PCh. 2.2 - Prob. 19PCh. 2.2 - Prob. 20PCh. 2.2 - Prob. 21PCh. 2.2 - Prob. 22PCh. 2.2 - Prob. 23PCh. 2.2 - Prob. 24PCh. 2.2 - Prob. 25PCh. 2.2 - Prob. 26PCh. 2.2 - Prob. 27PCh. 2.2 - Prob. 28PCh. 2.2 - Prob. 29PCh. 2.2 - Prob. 30PCh. 2.2 - Prob. 31PCh. 2.2 - Prob. 32PCh. 2.2 - Prob. 33PCh. 2.2 - Prob. 34PCh. 2.2 - Prob. 35PCh. 2.3 - Prob. 1PCh. 2.3 - Prob. 2PCh. 2.3 - Prob. 3PCh. 2.3 - Prob. 4PCh. 2.3 - Prob. 5PCh. 2.3 - Prob. 6PCh. 2.3 - Prob. 7PCh. 2.3 - Prob. 8PCh. 2.3 - Prob. 9PCh. 2.3 - Prob. 10PCh. 2.3 - Prob. 11PCh. 2.3 - Prob. 12PCh. 2.3 - Prob. 13PCh. 2.3 - Prob. 14PCh. 2.3 - Prob. 15PCh. 2.3 - Prob. 16PCh. 2.3 - Prob. 17PCh. 2.3 - Prob. 18PCh. 2.3 - Prob. 19PCh. 2.3 - Prob. 20PCh. 2.3 - Prob. 21PCh. 2.3 - Prob. 22PCh. 2.3 - Prob. 23PCh. 2.3 - Prob. 24PCh. 2.3 - Prob. 25PCh. 2.3 - Prob. 26PCh. 2.3 - Prob. 27PCh. 2.3 - Prob. 28PCh. 2.3 - Prob. 29PCh. 2.3 - Prob. 30PCh. 2.3 - Prob. 31PCh. 2.3 - Prob. 32PCh. 2.3 - Prob. 33PCh. 2.3 - Prob. 34PCh. 2.3 - Prob. 35PCh. 2.3 - Prob. 36PCh. 2.3 - Prob. 37PCh. 2.3 - Prob. 38PCh. 2.3 - Prob. 39PCh. 2.3 - Prob. 40PCh. 2.3 - Prob. 41PCh. 2.3 - Prob. 42PCh. 2.3 - Prob. 43PCh. 2.3 - Prob. 44PCh. 2.3 - Prob. 45PCh. 2.3 - Prob. 46PCh. 2.3 - Prob. 47PCh. 2.3 - Prob. 48PCh. 2.3 - Prob. 49PCh. 2.3 - Prob. 50PCh. 2.3 - Prob. 51PCh. 2.3 - Prob. 52PCh. 2.3 - Prob. 53PCh. 2.3 - Prob. 54PCh. 2.3 - Prob. 55PCh. 2.3 - Prob. 56PCh. 2.3 - Prob. 57PCh. 2.3 - Prob. 58PCh. 2.3 - Prob. 59PCh. 2.3 - Prob. 60PCh. 2.3 - Prob. 61PCh. 2.3 - Prob. 62PCh. 2.3 - Prob. 63PCh. 2.3 - Prob. 64PCh. 2.3 - Prob. 65PCh. 2.3 - Prob. 66PCh. 2.3 - Prob. 67PCh. 2.3 - Prob. 68PCh. 2.3 - Prob. 69PCh. 2.4 - Prob. 1PCh. 2.4 - Prob. 2PCh. 2.4 - Prob. 3PCh. 2.4 - Prob. 4PCh. 2.4 - Prob. 5PCh. 2.4 - Prob. 6PCh. 2.4 - Prob. 7PCh. 2.4 - Prob. 8PCh. 2.4 - Prob. 9PCh. 2.4 - Prob. 10PCh. 2.4 - Prob. 11PCh. 2.4 - Prob. 12PCh. 2.4 - Prob. 13PCh. 2.4 - Prob. 14PCh. 2.4 - Prob. 15PCh. 2.4 - Prob. 16PCh. 2.4 - Prob. 17PCh. 2.4 - Prob. 18PCh. 2.4 - Prob. 19PCh. 2.4 - Prob. 20PCh. 2.4 - Prob. 21PCh. 2.4 - Prob. 22PCh. 2.4 - Prob. 23PCh. 2.4 - Prob. 24PCh. 2.4 - Prob. 25PCh. 2.4 - Prob. 26PCh. 2.4 - Prob. 27PCh. 2.4 - Prob. 28PCh. 2.4 - Prob. 29PCh. 2.4 - Prob. 30PCh. 2.4 - Prob. 31PCh. 2.4 - Prob. 32PCh. 2.4 - Prob. 33PCh. 2.4 - Prob. 34PCh. 2.4 - Prob. 35PCh. 2.4 - Prob. 36PCh. 2.5 - Prob. 1PCh. 2.5 - Prob. 2PCh. 2.5 - Prob. 3PCh. 2.5 - Prob. 4PCh. 2.5 - Prob. 5PCh. 2.5 - Prob. 6PCh. 2.5 - Prob. 7PCh. 2.5 - Prob. 8PCh. 2.5 - Prob. 9PCh. 2.5 - Prob. 10PCh. 2.5 - Prob. 11PCh. 2.5 - Prob. 12PCh. 2.5 - Prob. 13PCh. 2.5 - Prob. 14PCh. 2.5 - Prob. 15PCh. 2.5 - Prob. 16PCh. 2.5 - Prob. 17PCh. 2.5 - Prob. 18PCh. 2.5 - Prob. 19PCh. 2 - Prob. 1SYUCh. 2 - Prob. 2SYUCh. 2 - Prob. 3SYUCh. 2 - Prob. 4SYUCh. 2 - Prob. 5SYUCh. 2 - Prob. 6SYUCh. 2 - Prob. 7SYUCh. 2 - Prob. 8SYUCh. 2 - Prob. 9SYUCh. 2 - Prob. 10SYUCh. 2 - Prob. 11SYUCh. 2 - Prob. 12SYUCh. 2 - Prob. 13SYUCh. 2 - Prob. 14SYUCh. 2 - Prob. 15SYUCh. 2 - Prob. 16SYUCh. 2 - Prob. 17SYUCh. 2 - Prob. 18SYUCh. 2 - Prob. 19SYUCh. 2 - Prob. 20SYUCh. 2 - Prob. 21SYUCh. 2 - Prob. 22SYUCh. 2 - Prob. 23SYUCh. 2 - Prob. 24SYUCh. 2 - Prob. 25SYUCh. 2 - Prob. 26SYUCh. 2 - Prob. 27SYUCh. 2 - Prob. 28SYUCh. 2 - Prob. 29SYUCh. 2 - Prob. 30SYUCh. 2 - Prob. 31SYUCh. 2 - Prob. 32SYUCh. 2 - Prob. 33SYUCh. 2 - Prob. 34SYUCh. 2 - Prob. 35SYUCh. 2 - Prob. 36SYUCh. 2 - Prob. 37SYUCh. 2 - Prob. 38SYUCh. 2 - Prob. 39SYUCh. 2 - Prob. 40SYUCh. 2 - Prob. 41SYUCh. 2 - Prob. 42SYUCh. 2 - Prob. 43SYUCh. 2 - Prob. 44SYUCh. 2 - Prob. 45SYUCh. 2 - Prob. 46SYUCh. 2 - Prob. 47SYUCh. 2 - Prob. 48SYUCh. 2 - Prob. 49SYUCh. 2 - Prob. 50SYUCh. 2 - Prob. 51SYUCh. 2 - Prob. 52SYUCh. 2 - Prob. 53SYUCh. 2 - Prob. 54SYUCh. 2 - Prob. 55SYUCh. 2 - Prob. 1FOTCh. 2 - Prob. 2FOTCh. 2 - Prob. 3FOTCh. 2 - Prob. 4FOTCh. 2 - Prob. 5FOTCh. 2 - Prob. 6FOTCh. 2 - Prob. 7FOTCh. 2 - Prob. 8FOTCh. 2 - Prob. 9FOTCh. 2 - Prob. 10FOTCh. 2 - Prob. 11FOTCh. 2 - Prob. 12FOTCh. 2 - Prob. 13FOTCh. 2 - Prob. 14FOTCh. 2 - Prob. 15FOTCh. 2 - Prob. 16FOTCh. 2 - Prob. 17FOTCh. 2 - Prob. 18FOTCh. 2 - Prob. 19FOTCh. 2 - Prob. 20FOTCh. 2 - Prob. 21FOTCh. 2 - Prob. 22FOTCh. 2 - Prob. 23FOTCh. 2 - Prob. 24FOTCh. 2 - Prob. 25FOTCh. 2 - Prob. 26FOTCh. 2 - Prob. 27FOTCh. 2 - Prob. 28FOTCh. 2 - Prob. 29FOTCh. 2 - Prob. 30FOTCh. 2 - Prob. 31FOTCh. 2 - Prob. 32FOTCh. 2 - Prob. 33FOTCh. 2 - Prob. 34FOTCh. 2 - Prob. 35FOTCh. 2 - Prob. 36FOTCh. 2 - Prob. 37FOTCh. 2 - Prob. 38FOTCh. 2 - Prob. 39FOTCh. 2 - Prob. 40FOTCh. 2 - Prob. 41FOTCh. 2 - Prob. 42FOTCh. 2 - Prob. 43FOT
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