Find the indicated limit, if it exists.

Find The Indicated Limit, If It Exists.

Answers

Answer 1

Answer:

[tex]\displaystyle \lim_{x \to -8} f(x) = 1[/tex]

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Constant]:                                                                                             [tex]\displaystyle \lim_{x \to c} b = b[/tex]

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Property [Addition/Subtraction]:                                                                   [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]

Step-by-step explanation:

*Note:

When you graph the function, the left-hand and right-hand limit does equal the same.

Step 1: Define

[tex]\displaystyle f(x) = \left \{ {{x + 9, x < -8} \atop {-7 - x, x \geq -8}} \right.[/tex]

Step 2: Find Limit

Substitute in function [Limit]:                                                                        [tex]\displaystyle \lim_{x \to -8} f(x) = \lim_{x \to -8} (-7 - x)[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]:                           [tex]\displaystyle \lim_{x \to -8} f(x) = -7 - (-8)[/tex]Simplify:                                                                                                         [tex]\displaystyle \lim_{x \to -8} f(x) = 1[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits


Related Questions

The park was muddy and the dogs’ paws got muddy while playing. Jen has wipes to clean the dogs’ paws. It takes one wipe to clean each paw. How many wipes will they need?

pls give me the correct answer

Answers

Answer:

A regular dog has 4 legs so it has 4 paws. If each paw needs one wipe Jen will need 4 wipes.

Jen will need 4 wipes for each paw

Hoy vamos de excursión con la escuela y nos ha tocado hacer los bocadillos para toda la clase. Si para hacer los bocadillos para mis 4 hermanos gastamos 2 barras de pan, ¿cuántas barras de pan necesitaremos para hacer los bocadillos de los 24 alumnos que hay en clase?Regla de tres

Answers

Answer:

12barras

Step-by-step explanation:

Hoy vamos a hacer una excursión con la escuela y tuvimos que hacer sándwiches para toda la clase. Si gastamos 2 hogazas de pan para hacer sándwiches para mis 4 hermanos, ¿cuántas hogazas de pan necesitaremos para hacer sándwiches para los 24 estudiantes de la clase?

De la pregunta anterior:

4 personas = 2 barras de pan

24 personas = x

Multiplicar cruzada

4 × x = 24 × 2 barras de pan

x = 24 × 2 barras de pan / 4

x = 12 barras de pan

A line passes through the points (3, –1) and (5, 4). What is the slope of the line?

Answers

Answer:

D) 5/2

Step-by-step explanation:

(3, –1) and (5, 4)

Slope:

m=(y2-y1)/(x2-x1)

m=(4 + 1)/(5 - 3)

m= 5/2

Answer:

5/2

Step-by-step explanation:

To find the slope, we can use the slope formula

m= (y2-y1)/(x2-x1)

   = (4 - -1)/(5 - 3)

   = (4+1)/(5-3)

   = 5/2

Which expression is represented by this model

Answers

Answer:

A

Step-by-step explanation:

The distance between 0 and 4/6 is 4/6. This distance is repeted two times

so we have 4/6 + 4/6 or 2 x 4/6

Pam had some toy cars. She got 4 more cars. Then her friend gave her 2 more cars. Now Pam has 18 toy cars in all. Which equation shows this word problem? O A. A. 0 +4+2 = 18 О B. D +4- 2 = 18 O + C. 4+ 2 + 18 = 0 O D. 4+2 – 18 = 1​

Answers

A behsnsnnfnfnfhdbdbdnd hdjdns. Dhjdns fjjd rush d end d s

please provide a solution

Answers

Answer: Based on hint and given formula, we can complete the problem. The question asks for square feet of grass so we know that we are solving for the area, A. It also tells us the height (looking downward) of the field is 75 ft,h, while the two bases are 125 ft and 81 ft (b1 and b2). So we can solve the equation. A = 75((125+81)/2) A = 75(206/2) A = 75(103) A = 7725 The area of the field is 7725 square feet.Step-by-step explanation: Hope it helps

I NEED AN ANSWER ASAP PLEASE!!!

Answers

Answer:

40%  properties  are Semi-detached

Step-by-step explanation:

Given,

Percentage of Bungalow = 10%

Percentage of Detached properties = 30%

Percentage of Apartments = 20%

∴Total percentage of properties deducting the  semi-detached properties

= (10 + 30 + 20) %

= 60%

∴ Percentage of semi detached properties = (100 - 60) %

                                                                        = 40%

So, 40% properties are Semi-detached.

HELP WILL COUNT BRAINLIEST

Answers

The answer is D, its equivalent

Find the circumference of the given circle given a diameter of 40 cm.
Use 3.14 as an approximation of Pi.

Answers

Answer:

c. 125.6

Step-by-step explanation:

Pi= 3.14

r= d/2 = 40/2 = 20

[tex]2\pi \: r[/tex]

= 2 × 3.14 × 20

=125.6

rationalise 1/√5 please tell​

Answers

Answer:

Step-by-step explanation:

1/[tex]\sqrt{5}[/tex]

=1[tex]\sqrt{5}[/tex] *[tex]\sqrt{5}[/tex]/[tex]\sqrt{5}[/tex]

=1*[tex]\sqrt{5}[/tex]/[tex]\sqrt{5}[/tex]*[tex]\sqrt{5}[/tex]

=1[tex]\sqrt{5}[/tex]/5

Find x in each image below. Simplify any radicals.

Answers

To Find :

The value of x.

Solution :

We know, when two chords intersect outside the circle.

[tex]21\times ( 21 + 45 ) = x \times ( x+5x)\\\\1386 = 6x^2\\\\x^2 = 231\\\\x = \sqrt{231}[/tex]

Hence, this is the required solution.

In the field of calculus there is an opposite function to differentiation. What is the name of this function that is used to determine the area under a curve?

Integration
Separation
Agglutination
Conglomeration

Answers

Answer:

Integration

General Formulas and Concepts:

Calculus

Integration

IntegralsIntegration TechniquesAntiderivativesArea under the curveApplication of Integration

Step-by-step explanation:

Integration is known as the "opposite" to differentiation. Integration is essential coined "antiderivatives" for being so.

Applications of Integration include finding the area under a curve; area between 2 curves; volumes of revolution; surface area for cartesian, parametric, and polar graphs; arc length for cartesian, parametric, and polar graphs; and the Integral Test for series convergence.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

find and interpret the slope

Answers

Answer:

y interpret is 60

slope 60/4=20x

hope this helps

have a good day :)

Step-by-step explanation:

If a=2i+4j, b=2i-5j.What is the vector equation of line AB?.

Answers

Answer:

9j

Step-by-step explanation:

vector AB means going to B from A.

= pos. final - pos. initial

= pos.B - pos.A

= (2i + 4j) - (2i - 5j)

= 2i + 4j - 2i + 5j

= 9j

PLEASE HELP GONNA FAIL WILL GIVE BRAINLESS

Answers

Answer: P = 166 units

Step-by-step explanation: Each point on the triangle has lines that are tangent to the circle in the triangle, meaning that those lines form a 90° angle to the middle point in the circle. There is also a rule that states if there are tangent lines coming from the points and if the points have at least one given side length, the other side will have the same side length. So if one side on point D is 41, then the other side connected to the point is 41. I added up all of the side lengths; 41 + 41 + 30 + 30 + 12 +12 = 166 units.

I hope this helps!


When a warehouse opened, it had an inventory of 6,000 items. Every month, the inventory increases by 3,000 items.
Which graph has the most appropriate scales and units for this situation?

Answers

Answer:

Step-by-step explanation: 90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you  

Given that f(x) = 3x - 2, g(x) = x2 + 3x and h(x) = 4.2^x​

Answers

i pray for you i hated this section and i wish i could help you:( the app photo math helped me!

A cube block has sides 8cm long. A cylindrical hole of radius 3.6 is drilled through the block. Find the volume of the block that remained

Answers

Answer:

186.45 cm^3

Step-by-step explanation:

Given data

Side lenght of cube block= 8cm

Radius of cylindrical hole= 3.6cm

Volume of entire Shape= l^3

Volume of entire Shape= 8*8*8

Volume of entire block= 512cm^3

Volume of cylindrical hole= πr^2h

Volume of cylindrical hole= 3.14*3.6^2*8

Volume of cylindrical hole= 3.14*12.96*8

Volume of cylindrical hole= 325.55cm^3

Hence the volume of the block

=volume of entire shape- volume of cylinder

=512-325.55

=186.45 cm^3

What are the solutions to the equation x² + 16x + 14 = 0?

Answers

Answer:

-8+5√2 and -8-5√2

Step-by-step explanation:

Given the expression x² + 16x + 14 = 0

USing the general formulas

x = -16±√16²-4(14)/2

x = -16±√256-56/2

x = -16±√200/2

x = -16±10√2/2

x = -8±5√2

Hence the required solutions are -8+5√2 and -8-5√2

Can somebody help with this

Answers

Answer:

B

Step-by-step explanation:

Domain is the x value and it is asking your for the coordinates with the same x value.

Help !Which of the following functions are linear?
Function A
Function b
Function a and b
Or none of the above

Answers

Answer:

function A

Step-by-step explanation:

_______________

Function A is correct one

Points A, B, C, and D are the vertices of a square. Points E and F are the center of two congruent semicircles that are tangent to each other at point G. Which value is closest to the area of the shaded regions? ​

Answers

Answer:

8 sq units

Step-by-step explanation:

to find the area of shaded region:

area of square minus sum of areas of each semi-circle

A(square) = 6² = 36

A (semi-circle) = πr²/2

= π3²/2

= 4.5π

Since there are two semi-circles, that makes one complete circle with an area of 9π

A(circle) ≈ 28 sq units

36-28 = 8 sq units

5. A raincloud contains 2500 litres of water. The cloud is decreasing in size at
a rate of 4.3% per hour. Calculate the volume of water in the cloud in 8
hours time.

Answers

Answer:

Volume 1758.88 litres

Step-by-step explanation:

[tex]P = 2500. \ r = 4.3\% = \frac{4.3}{100} = 0.043, t = 8\\\\Volume = P(1 - r)^t\\\\[/tex]

            [tex]= 2500(1-0.043)^8\\\\= 2500 \times 0.70355\\\\= 1758.88 \ litres[/tex]

Could you help ? It says “ a nursery plants a new tree and attaches a guy wire to help support the tree while it’s roots take hold. An eight foot wire is attached to the tree and to a stake in the ground the angle of elevation of the connection with the tree is 42 degrees . Find the nearest tenth of a foot, the height of the connection point on the tree” .

Answers

Answer:

5.4'

Step-by-step explanation:

See diagram attached.

The 8' wire is the hypotenuse of the triangle, with a base angle of 42°.

Hence the height is the length of the hypotenuse multiplied by sin(42°)

H = 8sin(42°) = 8 *0.6691 = 5.353'

(see similar or identical question 23903470)

Please help with this ASAP

Answers

Answer:

7w^3/5v

Step-by-step explanation:

42v^3w^4/30v^4w

42 = 6 * 7

30 = 6*5 , factor

6*7v^3w^4/6*5v^4w

6 is common, cancel

7v^3w^4/5v^4w

simplify w^4/w = w^3

v^3/v^4 = 1/v

therefore, 7w^3/5v is the answer

26. What is the approximate length of RS 7
18 in
S
21 in
R
A. 9.5 in
B. 10.8 In
C 12.1 In
D. 12.8 In

Answers

The correct answer would have been b, that is the way I solved it
The correct answer would be B

using the triangle 45o -45o -90o theorem solve this triangle. please​

Answers

Answer:

The length of the leg is 11 units.

Step-by-step explanation:

The triangle 45 - 45 - 90 theorem states that the length of the hypotenuse is [tex]\sqrt{2}[/tex] times of the length of any of the legs. Hence, we get the following expression:

[tex]h = \sqrt{2} \cdot l[/tex] (1)

Where:

[tex]l[/tex] - Length of the leg, in units.

[tex]h[/tex] - Hypotenuse, in units.

If we know that [tex]h = 11\sqrt{2}[/tex], then the length of the leg is:

[tex]l = \frac{h}{\sqrt{2}}[/tex]

[tex]l = 11[/tex]

The length of the leg is 11 units.

Write each number as a fraction or Mixed number.
(Please help! I'm trying to promote!)

Answers

Answer:

0.7 repeating is 7/9

0.04 repeating is 4/99

4.45 repeating 4 4/11

2.19191919...... is 2 19/99

hope this helps

have a good day :)

Step-by-step explanation:

A furniture designer builds a trapezoidal desk with a semicircular cutout. What is the area of the desk?

Answers

Answer:

[tex]Area = 26478cm^2[/tex]

Step-by-step explanation:

Given

See attachment for desk

Required

The area

First, calculate the area of the semicircular cutout

[tex]Area = \frac{\pi r^2}{2}[/tex]

Where

[tex]r = 60cm[/tex]

So:

[tex]A_1 = \frac{3.14 * 60^2}{2}[/tex]

[tex]A_1 = \frac{11304}{2}[/tex]

[tex]A_1 = 5652cm^2[/tex]

Next, the area of the complete trapezium

[tex]Area= \frac{1}{2}(a + b) * h[/tex]

Where

[tex]a = 300[/tex]

[tex]b = 2 * r = 2 * 60 = 120[/tex]

[tex]h = 153[/tex]

So:

[tex]A_2 = \frac{1}{2} * (300 + 120) * 153[/tex]

[tex]A_2 = \frac{1}{2} * 420 * 153[/tex]

[tex]A_2 = 32130cm^2[/tex]

The area of the desk is:

[tex]Area = A_2 - A_1[/tex]

[tex]Area = 32130cm^2 - 5652cm^2[/tex]

[tex]Area = 26478cm^2[/tex]

PLS HELP I WILL GIVE BRIANLY!

Francine bought 3 skirts that cost $2500 each before the discount. What was her total after
the discount?​

Answers

What was the discount? There isn’t enough information for me to answer it
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