1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
gregori [183]
3 years ago
11

Use series to verify that

x}" align="absmiddle" class="latex-formula"> is a solution of the equation y' = y
Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
6 0

y = e^x\\\\\displaystyle y = \sum_{k=1}^{\infty}\frac{x^k}{k!}\\\\\displaystyle y= 1+x+\frac{x^2}{2!} + \frac{x^3}{3!}+\ldots\\\\\displaystyle y' = \frac{d}{dx}\left( 1+x+\frac{x^2}{2!} + \frac{x^3}{3!}+\frac{x^4}{4!}+\ldots\right)\\\\

\displaystyle y' = \frac{d}{dx}\left(1\right)+\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{2!}\right) + \frac{d}{dx}\left(\frac{x^3}{3!}\right) + \frac{d}{dx}\left(\frac{x^4}{4!}\right)+\ldots\\\\\displaystyle y' = 0+1+\frac{2x^1}{2*1} + \frac{3x^2}{3*2!} + \frac{4x^3}{4*3!}+\ldots\\\\\displaystyle y' = 1 + x + \frac{x^2}{2!}+ \frac{x^3}{3!}+\ldots\\\\\displaystyle y' = \sum_{k=1}^{\infty}\frac{x^k}{k!}\\\\\displaystyle y' = e^{x}\\\\

This shows that y' = y is true when y = e^x

-----------------------

  • Note 1: A more general solution is y = Ce^x for some constant C.
  • Note 2: It might be tempting to say the general solution is y = e^x+C, but that is not the case because y = e^x+C \to y' = e^x+0 = e^x and we can see that y' = y would only be true for C = 0, so that is why y = e^x+C does not work.
You might be interested in
#3) A skier is at the top of his hill ready to ski down. The skier is now located at
gladu [14]
The any would be -7/-3
4 0
2 years ago
Find the value of <img src="https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%5E%7B3%7D" id="TexFormula1" title="\frac{2}{3} ^{3}
olga nikolaevna [1]

Answer:

Step-by-step explanation:

5 0
3 years ago
2 Richard and Jason each begin filling pools at the same time.
alina1380 [7]

The quantity of the liquid in Richard's tank after 20 minutes will be 120 gallons and in Jason's tank will be 240 gallons.

<h3>What are gallons?</h3>

A gallon is a British unit which is used for the measurement of liquids that is equal to eight pints. In Britain, it is equal to about 4.546 litres. In America, it is equal to about 3.785 litres.

It is given in the question that:-

Richard fills his pool at a rate of 6 gallons per minute.

Jason's pool already contains 200 gallons, and he fills it at a rate of 2 gallons per minute.

After 20 minutes the amount of liquid in the tank will be:-

For Richard = 6 gallons per minute. x  20  minutes= 120 gallons

For Jason= 2 gallons per minute  x  20  =40 gallons

Jason has 200 gallons already in the tank

So it will become = 200+24=240 gallons.

Hence  quantity of the liquid in Richard's tank after 20 minutes will be 120 gallons and in Jason's tank will be 240 gallons.

To know more about Gallons follow

brainly.com/question/16691874

#SPJ1

7 0
2 years ago
What is the simplified expression for the expression below?
Viktor [21]

Answer:

-2x + 3

Step-by-step explanation:

-5x/5 - 20/5 - 4x/4 + 28/4 ➡-x - 4 -x +7 ➡-2x + 3

8 0
3 years ago
Indi bought a shirt for $30. He paid 7% sales tax. How much sales tax did Indie pay?​
ivann1987 [24]

<u>He paid $ 32.10 </u>

because

07 * 30 = <u>2.10 </u>

2.10 + 30 = <u>$ 32.10</u>

7 0
3 years ago
Other questions:
  • Set up equation for the following angles
    12·2 answers
  • Combine like terms in the expression below.<br> 99x+4.11xy+24y+33y−12x+9.08
    6·2 answers
  • Select all input values for which h(x)=2
    15·1 answer
  • What two numbers have a product of -168 and sum -22 ?​
    15·2 answers
  • Which expression is equivaien. to 6 (3x + 4)?
    9·1 answer
  • The ratio of boys to girls in Mr. Lee's Geography class is 3 to 5. If there are a total of 32 students in the class, how many of
    9·1 answer
  • 00
    6·1 answer
  • The net price of a hand phone after allowing trade discount of 20% was RM2,000. Find what is the list price of the hand phone.​
    10·1 answer
  • Give me the right answer please i will give u half of my points i have 320 pleaseee im in a test rn
    10·2 answers
  • When multiplying a vector by a positive scalar number, the vectors _____ stays the same
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!