Answer:
(a) See below.
(b) x = 0 or x = 1
(c) x = 0 removable, x = 1 non-removable
Step-by-step explanation:
Given rational function:
<u>Part (a)</u>
Substitute x = 2 into the given rational function:
Therefore, as the function is defined at x = 2, the function is continuous at x = 2.
<u>Part (b)</u>
Given interval: [-2, 2]
Logs of negative numbers or zero are undefined. As the numerator is the natural log of an <u>absolute value</u>, the numerator is undefined when:
|x - 1| = 0 ⇒ x = 1.
A rational function is undefined when the denominator is equal to zero, so the function f(x) is undefined when x = 0.
So the function is discontinuous at x = 0 or x = 1 on the interval [-2, 2].
<u>Part (c)</u>
x = 1 is a <u>vertical asymptote</u>. As the function exists on both sides of this vertical asymptote, it is an <u>infinite discontinuity</u>. Since the function doesn't approach a particular finite value, the limit does not exist. Therefore, x = 1 is a non-removable discontinuity.
A <u>hole</u> exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal.
Therefore, there is a hole at x = 0.
The removable discontinuity of a function occurs at a point where the graph of a function has a hole in it. Therefore, x = 0 is a removable discontinuity.
Answer:
14?
Not sure what you mean
Step-by-step explanation:
Answer:
It is both a relation and a function.
Step-by-step explanation:
Keith collected the names and ages of all of his classmates and organized them in the ordered pair (name, age).
Here, if we consider the name as the input and age is the output, then each and every different input there is a single output.
Because a single person can not have more than one age.
Therefore, it is both a relation and a function. (Answer)
Answer:
The ira will contain $228,278.05 when he retires at age 65. This is 6.04 times the amount of money he deposited.
Step-by-step explanation:
In order to solve this problem, we can make use of the following formula:
![FV=PMT[\frac{(1+i)^{n}-1}{i}]](https://tex.z-dn.net/?f=FV%3DPMT%5B%5Cfrac%7B%281%2Bi%29%5E%7Bn%7D-1%7D%7Bi%7D%5D)
Where:
FV= Future value of the ira
PMT= the amount of money you deposit each month
i= is the interest rate per period
n=number of periods
in this case we will assume the interest will be compounded each month.
So:
FV this is what we need to know.
PMT= $75 the amount he will deposit each month
t = 42 years,
this is 65-23=42
n=42 years * 12 months/year = 504 months
i=0.07/12
So we can now use the given formula:
![FV=75[\frac{(1+\frac{0.07}{12})^{504}-1}{\frac{0.07}{12}}]](https://tex.z-dn.net/?f=FV%3D75%5B%5Cfrac%7B%281%2B%5Cfrac%7B0.07%7D%7B12%7D%29%5E%7B504%7D-1%7D%7B%5Cfrac%7B0.07%7D%7B12%7D%7D%5D)
So we get:
FV=$228,278.05
which is the amount of money he will have after 42 years.
In total, he deposited:
$75*504months = $37,800
so he will have:
times the amount of money he deposited throughout this time.
The awnser is F) This account earns 4% compounding interest.
Hope it helps :)
