The concentration C t (in ng/mL) of a drug in the bloodstream t hours after ingestion is modeled by C t = 500 t t 3 + 100 a. Graph the function y = C t and the line y = 4 on the window 0 , 32 , 4 by 0 , 15 , 3 . b. Use the Intersect feature to approximate the point(s) of intersection of y = C t and y = 4. Round to 1 decimal place if necessary. c. To avoid toxicity, a physician may give a second dose of the medicine once the concentration falls below 4 ng/mL for increasing values of t . Determine the times at which it is safe to give a second dose. Round to 1 decimal place.
The concentration C t (in ng/mL) of a drug in the bloodstream t hours after ingestion is modeled by C t = 500 t t 3 + 100 a. Graph the function y = C t and the line y = 4 on the window 0 , 32 , 4 by 0 , 15 , 3 . b. Use the Intersect feature to approximate the point(s) of intersection of y = C t and y = 4. Round to 1 decimal place if necessary. c. To avoid toxicity, a physician may give a second dose of the medicine once the concentration falls below 4 ng/mL for increasing values of t . Determine the times at which it is safe to give a second dose. Round to 1 decimal place.
Solution Summary: The author explains how to graph the function y=C(t) and the line
The concentration
C
t
(in ng/mL) of a drug in the bloodstream t hours after ingestion is modeled by
C
t
=
500
t
t
3
+
100
a. Graph the function
y
=
C
t
and the line
y
=
4
on the window
0
,
32
,
4
by
0
,
15
,
3
.
b. Use the Intersect feature to approximate the point(s) of intersection of
y
=
C
t
and
y
=
4.
Round to 1 decimal place if necessary.
c. To avoid toxicity, a physician may give a second dose of the medicine once the concentration falls below 4 ng/mL for increasing values of
t
. Determine the times at which it is safe to give a second dose. Round to 1 decimal place.
Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b).
x-a
f(x)=
1 - cos (4x-4)
3(x-1)²
; a = 1
a. Use a graphing utility to graph f. Select the correct graph below..
A.
W
→
✓
Each graph is displayed in a [- 1,3] by [0,5] window.
B.
in
✓
○ C.
und
☑
Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
x-1
○ A. The limit appears to be approximately ☐ .
(Round to the nearest tenth as needed.)
B. The limit does not exist.
b. Evaluate f(x) for values of x near 1 to support your conjecture.
X
0.9
0.99
0.999
1.001
1.01
1.1
f(x)
○ D.
+
☑
(Round to six decimal places as needed.)
Does the table from the previous step support your conjecture?
A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…
x²-19x+90
Let f(x) =
.
Complete parts (a) through (c) below.
x-a
a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
x→a+
○ A.
a=
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There are no values of a for which the limit equals a finite number.
b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
x→a+
A.
(Type integers or simplified fractions)
C. There are no values of a that satisfy lim f(x) = ∞.
+
x-a
c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
x→a+
A. Either a
(Type integers or simplified fractions)
B.
Sketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the following conditions.
f(2)=0
f(4) is undefined
lim f(x)=1
X-6
lim f(x) = -∞
x-0+
lim f(x) = ∞
lim f(x) = ∞
x-4
_8
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