93. Let f(x) = 3x - 1 and g(x) = x + 5. Evaluate the following limits. (a) lim x→3 f(g(x)]
(b) lim x→3 g[f(x)]

Answers

Answer 1

Answer:

a) 23 and b) 13

Step-by-step explanation:

I. If f(g(x)) is composit function

Find fog and gof

     fog = 3(g) - 1

           = 3(x+5) -1

           = 3x + 15 -1

           = 3x + 14

    gof = (f) + 5

          = (3x - 1) +5

          = 3x + 4

II. Fill in a) and b) question

            lim x -> 3 fog

           = 3(x) + 14

           = 3(3) + 14

          = 9 + 14

       a)  = 23

            lim x-> 3 gof

           = 3x + 4

           = 3(3) + 4

           = 9 + 4

        b)  = 13

Got more question or something to discuss, leave comment below


Related Questions

George gets paid £2,100 per month. Assuming he worked every month of the last year, how much would he earn in one year?​

Answers

Answer:

In one month he earn €2,100

He worked whole year

1 year = 12 months

So,

George earning is 12 months = 12 × Earning of one month

=> 2100 × 12

=> 25200

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Answer:

y = 1/2 x - 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

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Step-by-step explanation:

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Could someone do 14,15,and 16 for me? It would really help me out. Thank you!

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Answer:

Step-by-step explanation:

13) LCM of 20 , 5 is 20

Find equivalent fraction for 2/5 with denominator 20

[tex]\dfrac{2}{5}=\dfrac{2*4}{5*4}=\dfrac{8}{20}[/tex]

Now compare

[tex]\dfrac{7}{20} \ < \dfrac{8}{20}\\\\\dfrac{7}{20} \ < \dfrac{2}{5}[/tex]

14) Convert fraction to decimal

[tex]\dfrac{1}{8}= 0.125[/tex]

0.15  > 0.125

[tex]0.15 \ > \dfrac{1}{8}[/tex]

15) 0.5 , -1/7  , -0.2  ; 1/3

[tex]\dfrac{-1}{7}=-0.14\\\\\dfrac{1}{3}=0.3\\[/tex]

0.5, - 0.14 , -0.2  ; 0.3

Least to greatest:

-0.2 ;  - 0.14   ; 0.3  ; 0.5

Answer:

-0.2  ; [tex]\dfrac{-1}{7} \ ; \dfrac{1}{3} \ ; \ 0.5[/tex]

2 people eat 2 chicken in 2 days, how many chickens can 5 people eat in 5 days?

Answers

5 Peoples can eat 5 Chicken in 5 Days.

[tex]\mathfrak\purple{please \: mark \: me \: as \: brainliest}[/tex]

find the slope of the line that passes through each pair of points J(-4 8) and K(-4, 4)​

Answers

We will fight together no matter what I will always love you remind her be kind to othersI love you guys so much kisses and hugs

The coordinates of point T are (0,3). The midpoint of ST is (7. - 3). Find the coordinates of point S.
.
The other endpoint is
(Type an ordered pair.)

Answers

Answer:

(14,-9)

Step-by-step explanation:

Mrs. Jim earned $40.00 for selling tacos, and she spent $9.75 for supplies. The next day, she earned $35.00 in taco sales and she spent $12.50 for supplies. How much did Mrs. Jim earn and how much did she spend?

a
She earned $15 and she spent $2.75
b
She earned $22.25 and she spent $75
c
She earned $75 and she spent $22.25
d
She earned $75 and spent $23.75

Answers

The answer is C. She earned $75 and spent $22.25

We can take our totals that were earned before she started spending and combine them. On concurrent days she received a total of $75. She got $40 one day and $35 the next. In between those days she spent, $9.75 and $12.50. She spent a total of $22.25. Once again making the answer option C

an acute angle is an angle which is_______

Answers

Answer:

less then 90º

Step-by-step explanation:

an acute angle is an angle which is less then 90º

Less than a 90 degree angle

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The Value in cents of q quarters

Answers

Answer:

one quarter is 0.25c

so q=0.25c

Write the Roman Numeral CLXIV in standard form. Roman Numeral Standard Number 1 5 10 50 100 500 1,000 X L C D A) 169 B) 166 C) 164​

Answers

Answer:

164

Step-by-step explanation:

in standard form CLXIV IS 164

help me please urgent

Answers

Answer:

3+ x • {2x} + 5 = 858

Step-by-step explanation:

<33 hoped this helped !!!

during the movie fundraising event the concession stand at the auditorium sells popcorn fruit and drinks the price of a box of popcorn is 0.50 more than

Answers

Using the information in the exercise to develop the system of equations and using the substitution method, the following answers are found:

The system of the linear equations is P = F + 0.50, 2D = 3F - 0.50, and 2P + F + 3D = 7.75, where P = The price of a box of popcorn, D = The price of a drink, and F = The price of a piece of fruit. By other hand, the price of each item is: Popcorn = $1.50, Drink = $1.25, and Fruit = $1.

Solution of the system of equations by the Substitution Method.

Taking into account the information given in the exercise, we can write the next equations:

P = F + 0.502D = 3F - 0.502P + F + 3D = 7.75

Where:

P = The price of a box of popcorn.D = The price of a drink.F = The price of a piece of fruit.

Since all equations have the variable F, we are going to use it as a key variable to represent the other variables in terms of F.

In the first equation we should not do anything, since P is in terms of F, in the second case the variable D is also in terms of F, but we need to find the value of just D, by this:

2D = 3F - 0.50D = (3F - 0.50) / 2D = 1.5F - 0.25

We proceed to substitute the first and second equations in the third equation:

2P + F + 3D = 7.752 (F + 0.50) + F + 3 (1.5F - 0.25) = 7.75

And we solve for the variable F:

2F + 1 + F + 4.5F - 0.75 = 7.757.5F + 0.25 = 7.757.5F = 7.75 - 0.257.5F = 7.5F = 7.5 / 7.5F = 1

Now, we can solve for the variable D with the second equation:

2D = 3F - 0.502D = 3 * (1) - 0.502D = 3 - 0.502D = 2.5D = 2.5 / 2D = 1.25

Finally, we can solve for the variable P with the first equation:

P = F + 0.50P = 1 + 0.50P = 1.50

So, we have the price of each item:

Popcorn = 1.50Drink = 1.25Fruit = 1

If you want to see another exercise solved by the substitution method, you can see this link: https://brainly.com/question/22340165?referrer=searchResults

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Answers

Step-by-step explanation:

5(12+8)...

if my answer helps you than mark me as brainliest.

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Answers

Answer:

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Step-by-step explanation:

Given sequence:

1/8, 2/7, 1/2, 4/5

Rewrite as:

1/8, 2/7, 3/6, 4/5

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or

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Recreate

1/8,2/7,3/6,4/5

We can see

The denominator is decreasing by 1 and numerator is increasing by 1

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Next term

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help me solve these please. Im in integrated math 2

Answers

Answer:

1.

[tex] \frac{2}{5} = \frac{x}{15} \\ \\ 5x = 2 \times 15 \\ 5x =30 \\ x = \frac{30}{5} \\ x = 6[/tex]

2.

[tex] \frac{4}{3} = \frac{x}{7} \\ 3x = 4 \times 7 \\ 3x = 28 \\ x = \frac{28}{3} \\ x = 9.33 [/tex]

3.

[tex] \frac{7}{5} = \frac{28}{x} \\ 7x = 5 \times 28 \\ 7x = 140 \\ x = \frac{140}{7} \\ x = 20[/tex]

4.

[tex] \frac{11}{4} = \frac{5}{x} \\ 11x = 5 \times 4 \\ 11x = 20 \\ x = \frac{20}{11} \\ x = 1.8[/tex]

I hope I helped you^_^

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Answers

Step-by-step explanation:

7x - 5 = 8

7x = 8 + 5

7x = 13 (divide both sides by 7 to get x)

7x/7 = 13/7

x = 1.85714285714

Answer these too questions plz

Answers

Answer:

Closed numbers

Monomial

Step-by-step explanation:

Closed numbers are the only that makes sense

Anything times 0 is 0 thus it is only 3y which makes it a monomial

I kinda need help with this

Answers

Answer:

x = 1

Step-by-step explanation:

f(x) = 3 or y = 3

Locate y = 3 on the y- axis , go horizontally across to meet the line at (1, 3 )

Then

When f(x) = 3 , x = 1


7. Is 5.787787778... a rational or irrational number?
Explain.

Answers

Answer:

Rational ...................

Step-by-step explanation:

A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333 (the threes go on forever). However, one third can be express as 1 divided by 3, and since 1 and 3 are both integers, one third is a rational number

(10 points) How many proportional relationships are shown in the coordinate plane

Answers

Answer:

D) 3

Step-by-step explanation:

There are 3 lines/graphs

I hope this helps!

find the measure of the missing angle ​

Answers

Answer:

127°

Step-by-step explanation:

180=53+x

127=x

A straight line is 180°

I hope this helps!

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Answers

i think thw answer is y

Answer:

y is larger.

Step-by-step explanation:

Along the same vertical line, 2 points have the same x value. So x=2 and y=4.

Can someone explain how to do integers since I have a test today? Also can someone please help me with the sheet too so I could understand? :)

Answers

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, . 09, and 5,643.1.

How many 4 inch cubes will fit in a 20 inch box?

Answers

Answer:

125

Step-by-step explanation:

If you mean a 20 inch cube box then the answer is 125. Since 4 inch cubes have dimensions 4x4x4 and 20 inch cubes have dimensions 20x20x20. Then we can find the answer by dividing 20x20x20 by 4x4x4 which is equal to 5x5x5 as 20/4 = 5. Therefore the answer is 5x5x5 which is 125.

x² + 4x from 5x² + x

Answers

That is,

(5x sq + x) - (x sq + 4x)

5x sq + x - (x sq + 4x)

5x sq - x sq + x - 4x

4x sq - 3x

help 100 points AND please DONT REPLY IF YOU DO NOT KNOW THE ANSWER
Thankyou!

Answers

Answer:

[tex]than k\: you[/tex]

6. (a) Convert 1101012 into decimal number system. b) Convert 456 into quinary number system. 7. (a) Find the mean of the given data. 2, 7, 9, 12, 15 (b) Factorize: a2 - 18a + 81 (C) Find the cube of; a+3​

Answers

Step-by-step explanation:

(110101)2=(53)10

This is the ans.

find the value of x and y​

Answers

Answer:

x=11

y=3

Step-by-step explanation:

(9x+25)=(13x-19)

9x+25 = 13x−19

9x+25-25 = 13x−19-25

9x=13x-44

9x-13x=13x-44-13x

-4x= -44

x=11

y= 180-(9x+25)

y= 180-(99+25)

y= 180-124 = 56

y= 56-5 = 51

y= 51/17

y= 3

Good luck

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