Mathematics, 02.10.2020 16:01 anonymous1813

Find limit. Please answer

Answers: 2

Show answers

Answers

Answer from: alex7881

$\displaystyle \lim_{x \to 2} \frac{x^8 - 256}{x - 2} = 1024$

General Formulas and Concepts:

Calculus

Limits

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

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

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

L'Hopital's Rule

Differentiation

DerivativesDerivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

We are given the following limit:

$\displaystyle \lim_{x \to 2} \frac{x^8 - 256}{x - 2}$

Substituting in x = 2 using the limit rule, we have:

$\displaystyle \lim_{x \to 2} \frac{x^8 - 256}{x - 2} = \frac{2^8 - 256}{2 - 2}$

Evaluating the result, we get an indeterminate form:

$\displaystyle \lim_{x \to 2} \frac{x^8 - 256}{x - 2} = \frac{0}{0}$

Since we have an indeterminate form, let's apply L'Hopital's Rule. Differentiate both the numerator and denominator respectively:

$\displaystyle \lim_{x \to 2} \frac{x^8 - 256}{x - 2} = \lim_{x \to 2} \frac{8x^7}{1}$

Simplify:

$\displaystyle \lim_{x \to 2} \frac{x^8 - 256}{x - 2} = \lim_{x \to 2} 8x^7$

Evaluate the limit using the limit rule:

$\displaystyle \lim_{x \to 2} 8x^7 = 8(2)^7$

Simplify:

$\displaystyle \lim_{x \to 2} 8x^7 = 1024$

And we have our answer.

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

Unit: Limits

Answer from: Quest

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

Answer from: Quest

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )
Ineed as soon as possible ! what is the approximate length of the minor arc de

Ineed as soon as possible ! what is the approximate length of the minor arc de

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 14:30, htorres2p8urw0

6.(q^9)^2 a. 2q^18 b. q^18 c. q^81 d. q^11 7.(6q^6)^-4 a. 6q^1296 b. 1296q^2 c. 1/1296q^24 d. 6q^-24 8. what is the value of 12x^-3 y^-1 for x = -1 and y = 5? a. -12/5 b.-10 c.-0 d.5/12 9. (y^-5)^10y^10 a. y^-60 b. y^60 c. y^-150 d. y^150 find the simplified form of each expression. 10. (4/7^5)^2 a.8/14^10 b.16/49^25 c.16/49y^10 d.8/14y^25 11. determine if the number 3.43 times 10^-6 is written in scientific notation. if not, explain. a. yes; the number is written scientific notation. b. no; the first factor is not a number between 1 and 10. c. no; it is not written as a number times a power of 10

Answers: 3

continue

Mathematics, 21.06.2019 20:00, hayleylaw2018

Which fraction is equal to 1hole and 2/5? a.3/5 b.75 c.57 d.73

Answers: 2

continue

Mathematics, 21.06.2019 22:00, taliyahjhonson1

The birth weights of newborn babies in the unites states follow in a normal distrubution with a mean of 3.4 kg and standard deviation of 0.6 kg. reaserches interested in studying how. children gain weights decide to take random samples of 100 newborn babies and calculate the sample mean birth weights for each sample

Answers: 1

continue

Mathematics, 21.06.2019 22:20, abbygriffin8575

Which graph has figures that can undergo a similarity transformation to justify that they are similar? (obviously not the third one)

Answers: 2

continue

You know the right answer?

Find limit. Please answer
...