Biocalculus
15th Edition
ISBN: 9781133109631
Author: Stewart, JAMES, Day, Troy
Publisher: Cengage Learning,
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Chapter 2, Problem 9E
(a)
To determine
To give: the value of given limits from the given graph.
(b)
To determine
To state: the equations of horizontal asymptotes of given graph.
(c)
To determine
To state: the equations of vertical asymptotes of given graph.
(d)
To determine
To find: the points of discontinuity of f.
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Students have asked these similar questions
3. Use given graph of f to state the value of each quantity, if it exists. If it doesn't exist
explain why.
(a) lim f(x)
(b) lim f(x)
X→0+
(c) lim f (=
X→0-
(d) lim f(x)
X→-3
-4
-2
4
2.
2. A portion of the graph of the function
y = f(x) is shown in the figure.
(a) State the domain and range of f.
(b) Find the values: f(-2) and f(3).
(c) Use the graph to determine each of
the limits:
(i) lim f(x); lim f(x); lim f(x)
x-2+
x-2-
x-2
(ii) lim f(x);
lim f(x);
x-3
lim f(x).
x+3
3. The graph of the function y = k(x) is
shown in the figure.
(a) Write a piecewise formula for the
function k.
(b) Evaluate the one-sided limits of
k at x = 1 algebraically, by using
your formula from part (a).
y=f(x)
1+
fif
1
-1-
2
1.5
1
4. Let f(x) = |x| and g(x) = x - 3.
(a) Determine the formulas for each of the related composite functions:
h(x) = (fog)(x) = f(g(x))
s(x) = (gof)(x) = g(f(x))
t(x) = (gofᵒg)(x) = g(f(g(x))).
5. (a) Find the values of x₁ and x₂ in the figure.
(b) Find the largest positive number 8 such that:
|-1|<0.1 whenever 0<|x-1|<8.
Hint:
Choose to be the minimum value of |x-1| for i = 1,2.
(b) Plot graphs of all the functions: f,h, s, and t in the same coordinate plane.
Use…
For the function h whose graph Is glven, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)
yA
A
4
-4
-2
4
(a)
lim h(x)
4
(ь)
lim h(x)
x- -3
lim h(x)
--3
(c)
(d)
h(-3)
3
(e)
lim h(x)
x- 0
1
(f)
lim h(x)
o+
-1
(g)
lim h(x)
XTO
(h)
h(0)
(i)
lim h(x)
x - 2
()
h(2)
(k)
lim h(x)
x- 5*
(1)
lim h(x)
Chapter 2 Solutions
Biocalculus
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