Which formula gives the area of Rectangle EFHG

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

For the sphere shown, r = 4.2 cm. What is its volume, to the nearest cubic centimeter?

DochEvi [55]

V = 4/3(pi)(r^3)
V = 4/3(pi)(4.2^3)
V = 310 cm^3

Good luck!

8 0

3 years ago

Given the trinomial 3x2 − 6x + 5, what is the value of the discriminant?

yan [13]

$\bf \begin{array}{llcccll}
& 3 x^2& -6 x& +5\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\\\\\\
discriminant\implies b^2-4ac\implies (-6)^2-4(3)(5)$

4 0

4 years ago

Which point is located on the x-axis ?

rjkz [21]

Answer:

Step-by-step explanation:

A coordinate grid has two perpendicular lines, or axes, labeled like number lines. The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the x-axis and y-axis intersect is called the origin.

8 0

3 years ago

Read 2 more answers

A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new televi

mestny [16]

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

P = 0.22

For the alternative hypothesis,

P < 0.22

This is a left tailed test

Considering the population proportion, probability of success, p = 0.22

q = probability of failure = 1 - p

q = 1 - 0.22 = 0.78

Considering the sample,

Sample proportion, p = x/n

Where

x = number of success = 230

n = number of samples = 1189

p = 230/1189 = 0.19

We would determine the test statistic which is the z score

z = (p - P)/√pq/n

z = (0.19 - 0.22)/√(0.22 × 0.78)/1189 = - 2.5

Recall, population proportion, p = 0.22

We want the area to the left of 0.22 since the alternative hypothesis is lesser than 0.22. Therefore, from the normal distribution table, the probability of getting a proportion < 0.22 is 0.00621

So p value = 0.00621

Since alpha, 0.01 > than the p value, 0.00621, then we would reject the null hypothesis.

Referring to the above, the null hypothesis will be rejected if the test statistic is - 2.5

8 0

4 years ago