Calculus Answers

Answer the following questions for the function
f(x)=x^3/(x^2−4)
defined on the interval [−19,16].

a.) Enter the x-coordinates of the vertical asymptotes of f(x) as a comma-separated list. That is, if there is just one value, give it; if there are more than one, enter them separated commas; and if there are none, enter NONE .

b)f(x) is concave up on the region=

Trace the curve (x²+y²)x=ay², a>0 stating all the properties used in the process

Suppose that it is given to you that
f′(x)=(x+6)(12−x)(x−15)

Then the first relative extremum (from the left) for f(x) occurs at x=

The function f(x) has a relative
?
at this point.

The second relative extremum (from the left) for f(x) occurs at x=

The function f(x) has a relative
?
at this point.

The third relative extremum (from the left) for f(x) occurs at x=

The function f(x) has a relative
?
at this point.

The first inflection point (from the left) for f(x) occurs at x=


The second inflection point (from the left) for f(x) occurs at x=

Use linear approximation, i.e. the tangent line, to approximate 3.76 as follows:
Let f(x)=x6. The equation of the tangent line to f(x) at x=4 can be written in the form y=mx+b
where m is:

and where b is:

Using this, we find our approximation for 3.76 is

A Spherical balloon is being inflated.
Find a general formula for the instantaneous rate of change of the volume V with respect to the radius r, given that V=4πr33.

Answer:


Find the rate of change of V with respect to r at the instant when the radius is r=5.

Answer:

Shown below are six statements about functions. Match each statement to one of the functions shown below which BEST matches that statement.

1. limx→6+f(x) and limx→6−f(x) both exist and are finite, but they are not equal.
2. The graph of y=f(x) has vertical tangent line at (6,f(6))
3. limx→6−f(x)=−∞.
4. limx→6+f(x) exists but limx→6−f(x) does not.
5. limx→6f(x)=∞.
6. limx→6f(x) exists but f is not continuous at 6.

A. f(x)=⎧⎩⎨⎪⎪⎪⎪cos(1x−6)02x+24if x<6if x=6if x>6
B. f(x)=⎧⎩⎨⎪⎪2x024−2xif x<6if x=6if x>6
C. f(x)=⎧⎩⎨⎪⎪2x02x−24if x<6if x=6if x>6
D. f(x)=x−6−−−−−√3
E. f(x)=1(x−6)2
F. f(x)=1x−6

The table below gives for the value of continuous function f at each x-value. Using the Intermediate Value Theorem and the information in the table, determine the smallest interval in which the function must have a root.

x f(x)
−5 −1.25
−4 −2.03
−3 −3.05
−2 3.01
−1 1.02
0 0.69
1 4.43
2 9.45
3 2.76
4 0.93
5 0.13
Answer (in interval notation):

Using the Intermediate Value Theorem and a calculator, find an interval of length 0.01 that contains a root of x5−x2+2x+3=0, rounding off interval endpoints to the nearest hundredth.

<x<

The function
f(x)=−2x3+15x2+84x+4
is increasing on the interval (
,
).

It is decreasing on the interval ( −∞,
) and the interval (
, ∞ ).

The function has a local maximum at
.

The volume of water entering a tank from a pump is related by the formula v=ah^3+bh^2+ch+d where is the height of the tank, a, b, c and d are constants.
Fine the condition for minimum and maximum water storage.