What is the value of the expression m^2 + 3m when m=4

Pls help this is pretty urgent

laiz [17]

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:

$f(x)=\dfrac{\ln |x-1|}{x}$

Part (a)

Substitute x = 2 into the given rational function:

$\begin{aligned}\implies f(2) & =\dfrac{\ln |2-1|}{2}\\\\ & =\dfrac{\ln 1}{2}\\\\ & =\dfrac{0}{2}\\\\ & =0\end{aligned}$

Therefore, as the function is defined at x = 2, the function is continuous at x = 2.

Part (b)

Given interval: [-2, 2]

Logs of negative numbers or zero are undefined. As the numerator is the natural log of an absolute value, 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].

Part (c)

x = 1 is a vertical asymptote. As the function exists on both sides of this vertical asymptote, it is an infinite discontinuity. Since the function doesn't approach a particular finite value, the limit does not exist. Therefore, x = 1 is a non-removable discontinuity.

A hole 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.

$\implies f(0)=\dfrac{\ln |0-1|}{0}=\dfrac{\ln 1}{0}=\dfrac{0}{0}$

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.

3 0

2 years ago

Read 2 more answers

How many inches are in 4 feet 3 inches?

V125BC [204]

52 because 4 feet is 48 inches 9 (which is like 1 feet is 12 inches) and 48 plus 4 equals 52

4 0

4 years ago

Read 2 more answers

GEOMETRY HELP! This is my last question and I don’t know what the answer is! Please help!

Angelina_Jolie [31]

Temporarily subdivide the given area into two parts: a large rectangle and a parallelogram. Find the areas of these two shapes separately and then combine them for the total area of the figure.

By counting squares on the graph, we see that the longest side of the rectangle is the hypotenuse of a triangle whose legs are 8 and 2. Applying the Pyth. Thm., we find that this length is √(8^2+2^2), or √68. Similarly, we find the the width of this rectangle is √(17). Thus, the area of the rectangle is √(17*68), or 34 square units.

This leaves the area of the parallelogram to be found. The length of one of the longer sides of the parallelogram is 6 and the width of the parallelogram is 1. Thus, the area of the parallelogram is A = 6(1) = 6 square units.

The total area of the given figure is then 34+6, or 40, square units.

7 0

4 years ago

CAN SOMEONE PLS ANSWER THIS QUESTION FAST I WILL MARK BRAINLIEST

Yakvenalex [24]

Answer:

B 5

Step-by-step explanation:

it is the same ratio as the red

8 0

2 years ago

How many different five digit members can be formed from the digits 5, 6, 7, 8 and 9 if digits can be repeated? If digits cannot

Dafna11 [192]

Answer:

Solution given:

5,6,7,8,9,

When repeated:

it has

5 ways for each

different five digit members can be formed from the digits:5*5*5*5*5=3125

When not repeated:

it has

5 ways for 1st

4 ways for 2nd

3 ways for 3rd

2 ways for 4th

1 ways for 5th

different five digit members can be formed from the digits:5*4*3*2*1=120

6 0

3 years ago