3. Are the points on the line part of the solution set or not?
a. Yes, they are part of the solution
b. No, they are not part of the solution
c. Maybe, they are part of the solution
d. None of the above​

Answer:

[tex]\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)}=1[/tex]

Step-by-step explanation:

We are given:

[tex]\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)[/tex]

And we want to evaluate it using L'Hopital's Rule.

First, using direct substitution, we will acquire:

[tex]=(1-1)^\ln(1)}=0^0[/tex]

Which is indeterminate.

In order to apply L'Hopital's Rule, we first need to manipulate the expression. We will let:

[tex]y=(x-1)^\ln(x)[/tex]

By taking the natural log of both sides:

[tex]\ln(y)=\ln(x)\ln(x-1)[/tex]

And by taking the limit as x approaches 1 from the right of both functions:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)=\lim_{x\to 1^+}\ln(x)\ln(x-1)[/tex]

Rewrite:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{\ln(x-1)}{\ln(x)^{-1}}[/tex]

Using direct substitution on the right will result in 0/0. Hence, we can now apply L'Hopital's Rule:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{1/(x-1)}{-\ln(x)^{-2}(1/x)}[/tex]

Simplify:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{1/(x-1)}{-\ln(x)^{-2}(1/x)}\Big(\frac{-x\ln(x)^2}{-x\ln(x)^2}\Big)[/tex]

Simplify:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}-\frac{x\ln(x)^2}{x-1}[/tex]

Now, by using direct substitution, we will acquire:

[tex]\displaystyle \Rightarrow -\frac{1\ln(1)^2}{1-1}=\frac{0}{0}[/tex]

Hence, we will apply L'Hopital's Rule once more. Utilize the product rule:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}-(\ln(x)^2+2x\ln(x))[/tex]

Finally, direct substitution yields:

[tex]\Rightarrow -(\ln(1)^2+2(1)\ln(1))=-(0+0)=0[/tex]

Thus:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)=0[/tex]

By the Composite Function Property for limits:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)=\ln( \lim_{x\to 1^+}y)=0[/tex]

Raising both sides to e produces:

[tex]\displaystyle e^{\ln \lim_{x\to 1^+}y}=e^0[/tex]

Therefore:

[tex]\displaystyle \lim_{x\to 1^+}y=1[/tex]

Substitution:

[tex]\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)}=1[/tex]

Step-by-step explanation:

its too blurry I can't see the numbers

Answer:

la eneria es muy importante

Answer:

15

Step-by-step explanation:

8^2 + b^2 = 17^2

64 + b^2 = 289

289 - 64 = 225

square root of 225 = 15

Answer:

13

Step-by-step explanation:

Given data

flat amount =$10

let the number of dogs walked be x

and let the money earned be y

y= 10+5x

for y= 75

let us find x

75= 10+5x

75-10= 5x

65= 5x

divide both sides by 5

x= 65/5

x=13

Hence the number of dogs is 13

Answer:

12 because u use the other shapes to reference your measurements.

Answer:

3√3−x=3√2x

Graph each side of the equation. The solution is the x-value of the point of intersection.

x≈0.46567646

image of graph

Step-by-step explanation:

Hope it is helpful.....

Answer:

you add 40+45

Step-by-step explanation:

40+45=85

then you subtract 180 - 85 = 95

then divide x into 95 that will give you x=95

Answer:

[tex]x > \frac{1}{4} [/tex]

Step-by-step explanation:

[tex]12x - 5 > - 2[/tex]

Lets add +5 in both the sides.

[tex] = > 12x - 5 + 5 > - 2 + 5[/tex]

[tex] = > 12x > 3[/tex]

Now lets divide 12 on both the sides.

[tex] = > \frac{12x}{12} > \frac{3}{12} [/tex]

[tex] = > x > \frac{1}{4} [/tex]

Answer:

hard to read, can you take another picture please?

Step-by-step explanation:

Answer:

eight hundred seventy-five thousand six hundred eighty-seven

hope this helps :)

Answer:

50 units.

Step-by-step explanation:

Answer:

it would be the third one ( 0,3)

Answer:

can you show us the graph

Answer:

d 5 tan theta

Step-by-step explanation:

5 sin theta x 1/cos theta

5 (sin theta/cos theta)

5 tan theta

Answer:

2

Step-by-step explanation:

por que el le dio 5 manzanas a jose y le quedaron 2

Answer:

x = 3

Step-by-step explanation:

Answer: x = 3

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

3(11 - 10) + 7 =

3 + 7 = 10

hope this helped

Answer:

l x w do the the math

Step-by-step explanation:

there

Answer:

u said free poinstt on that persons answer so Hi

Step-by-step explanation:

Answer:

7x+77

Step-by-step explanation:

7(x+11)

=(7)(x+11)

=(7)(x)+(7)(11)

=7x+77

The equivalent expression from the distributive property is 7x+77.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is 7(x + 11). From the distributive property, the expression will be calculated as:-

E = 7(x+11)

E=(7)(x+11)

E=(7)(x)+(7)(11)

E=7x+77

Therefore, the equivalent expression from the distributive property is 7x+77.

To know more about an expression follow

https://brainly.com/question/29083959

#SPJ6

Answer:ugh is there an picture maybe i can understand it better?

Step-by-step explanation:

Answer:

Its red becasue 1/2 is greater than all of them

The most likely color of the marble that will be chosen is red.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

Number of red marbles in the bag=1/2

Number of blue marbles in the bag=1/4

Number of green marbles in the bag=1/6

Number of yellow marbles in the bag=1/12

Now,

To determine the most likely color of the marble that will be chosen, we need to calculate the probability of selecting each color. The probability of selecting a red marble is 1/2, the probability of selecting a blue marble is 1/4, the probability of selecting a green marble is 1/6, and the probability of selecting a yellow marble is 1/12.

To compare the probabilities, we need to find a common denominator. The common denominator for 2, 4, 6, and 12 is 12. So, we can rewrite the probabilities as:

Probability of selecting a red marble = 6/12

Probability of selecting a blue marble = 3/12

Probability of selecting a green marble = 2/12

Probability of selecting a yellow marble = 1/12

Since the probability of selecting a red marble is the highest among all the colors, it is the most likely color to be chosen.

Therefore, by probability the answer will be red marble.

Learn more about probability here;

https://brainly.com/question/9326835

#SPJ5

The fractional form is 7/10.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

We have to divide 7 by 10.

The common factor for 7 and 10

7 = 7 x 1

and, 10= 2 x 5 x 1

so, there is only one factor common is 1.

Thus, the fraction is 7/10.

Learn more about Equivalent Fraction here:

https://brainly.com/question/29766013

#SPJ2