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
Evgesh-ka [11]
3 years ago
10

Estimate the maximum error made in approximating e^x by the polynomial 1 + x + {1}/{2}x^2 over the interval x of [-0.4,0.4].

Mathematics
1 answer:
kolezko [41]3 years ago
7 0
E^x = 1 + x + x² / 2 + x³/ 3! + x^4 / 4! + .....
       = (1 + x + x²/2 ) + x³   [ 1/6 + x /4! + x² / 5! + ....  ]
 Error =  e^x - (1+ x + x² )   =  x³ [  1/6 + x /4! + x² / 5! + ....  ]
          x / 4!  < x / 6            x² / 5!   <  x² / 6  and so on
         So if we replace all factorials by 1/6 ..
     error  <  x² [ 1/6 + x/6 + x²/6 + ... ]
             <  x² / 6    [ 1 + x + x² ..... ]
             < x² / 6    * 1 / (1 -x)    = x² / 6 (1-x)        if   x < 1
 maximum error  =  x² /6(1-x)  occurs at 0.4 or -0.4 in the given interval.
             =  0.0444444


You might be interested in
What is <br><br> 4.2 = c/8<br><br> And it would be a lot helpful
liberstina [14]

Step-by-step explanation:

c = 8 × 4.2 (move 8 from the denominator to the side where the 4.2 is - make c the subject)

c = 33.6

7 0
3 years ago
Read 2 more answers
Suppose you receive a $50 gift certificate to the citywide music and books store. All CDs at the store cost $9.99 and all books
Zanzabum
Whats the question I don't get it
7 0
3 years ago
Complete the solution of the equation. Find the value of y when x equals -3. 2x-5y =-21
vesna_86 [32]
The answer is y=3 ....

5 0
3 years ago
In a game a player draws and replaces a card from a deck 2 times. The possible outcomes and payouts are shown. What is the
Goshia [24]

<u>Given</u>:

Given that in a game a player draws and replaces a card from a deck 2 times.

The possible outcomes and payouts are given.

We need to determine the expected value for someone playing the game.

<u>Expected value:</u>

The expected value for someone playing the game can be determined by

EV=(\frac{26}{52})(\$ 20)+(\frac{52}{52})(\$4)+(\frac{52}{52})(\$ 0)+(\frac{26}{52})(-\$12)

Simplifying the values, we have;

EV=(\frac{1}{2})(\$ 20)+(1)(\$4)+(1)(\$ 0)+(\frac{1}{2})(-\$12)

Dividing the terms, we get;

EV=\$ 10+\$4+\$ 0+-\$6

Adding, we have;

EV=\$ 8

Thus, the expected value for someone playing the game is $8

3 0
3 years ago
If a bus can travel 194 miles in 4 hours how many miles can it travel in 1 hour l
Oksana_A [137]
In 1 hr the bus would have traveled 48.5 miles

7 0
3 years ago
Read 2 more answers
Other questions:
  • How much greater than m2+3mn−n2 is 4m2+5mn+6n2?<br> PLEASE HELP
    7·1 answer
  • Please hurry I need these fast
    14·1 answer
  • What is the estimate of the sum of 5/12 and 7/8?
    14·1 answer
  • A math class has girls and boys in the seventh grade and girls and boys in the eighth grade. The teacher randomly selects a seve
    8·1 answer
  • Please help with this one I’m almost done
    10·1 answer
  • I need help with this math problem not sure what to do?​
    11·1 answer
  • Solve the equation 5x - 8 = 9<br> Helpppp pleaseeee
    9·2 answers
  • Find the rate of change in a table
    11·2 answers
  • Solve the equation.<br><br> <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%28x%2B2%29%7D%20%3D%200" id="TexFormula1" title="\sqrt
    7·1 answer
  • you deposit 250 into an account at the end of 6 months your balance is 255 what is the simple annual interest rate
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!