Choose the one polynomial tgat are not closed under

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

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There are 65 campers at fun camp. only 53 campers brought sleeping bags. how many campers did not bring sleeping bags?

elena-s [515]

So you have to just subtract, 65-53=12 that didn't bring sleeping bags

8 0

3 years ago

The master family financed a computer that cost $1200. If the interest rate is 19%.how much will the family owe for the computer

Fantom [35]

The answer is $1219

Interest = Total amount * interest rate * time ( I=prt is the formula for calculating interest)

In this case,

Total amount = $1200

Interest rate= $ 0.19

Time span for which interest rate is being calculated= 1/12 (since the rate is yearly and we are calculating interest for a month)

Interest = 1200*0.19*1/12 = 19

So the total amount owned by family at the end of one month = original amount + interest = $1200 + $19 = $1219

6 0

3 years ago

Which shapes can be made from a planar cross section of a triangular pyramid? More than one can be correct: trapezoid, pentagon,

Jlenok [28]

Answer:

Triangle in isosceles, scalene or equilateral forms and

quadrilateral in trapezoid, rectangle or square forms

Step-by-step explanation:

Refer to pictures attached

Shapes can be formed are:

Trapezoid,

when perpendicular to base

Rectangle or square,

when angle cross section to base

Isosceles triangle,

when base is isosceles triangle and parallel cross section to base,

or angle cross section

Scalene triangle,

when base is scalene triangle and parallel cross section to base,

or angle cross section

Equilateral triangle,

when base is equilateral triangle and parallel cross section to base,

or angle cross section

7 0

3 years ago

In a two-digit number the units digit is three less than the tens digit. If the digits are reversed, the sum of the reversed num

makvit [3.9K]

Answer:

74.

Step-by-step explanation:

Let the number be xy.

Then from the given data

x = y + 3..........(1)

The numerical value of xy is 10x + y so the second equation is

10x + y + 10y + x = 121

11x + 11y = 121 Simplifying:

x + y = 11

x = -y + 11 .........(2) Adding equations (1) and (2):

2x = 14

x = 7

and therefore y = 7 - 3 = 4.

7 0

4 years ago

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