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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


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The sum of two consecutive mile markers on the interstate is 417417. Find the numbers on the markers
noname [10]

Hello from MrBillDoesMath!

Answer:

The first marker is labeled 208708; the second (consecutive) one 208709                  


Discussion:

Call the first mile marker "m". Then

m + (m+1) = 417417            => combine like terms

2m + 1 = 417417                 => subtract 1 from both sides

2m =  417416                     => divide both sides by 2

m  = 417416/2  = 208708                  

Note: m and (m+1) are consecutive as they immediately follow each other in the set of integers.

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The sum of three integers is 92. The second number is three times the first number. The third number is ten less than twice the
SVEN [57.7K]
Given,
The sum of three integers is 92

So,
Let,
The first integer be "x"
The second integer be "y"
The third integer be "z"

Now,
According to the question,
y = 3x          ..............equation (1)
z = 2x - 10    .............. equation (2)
x + y + z = 92 ..............equation (3)

Now,
Substituting the value of "y" and "z" from equation (1) and (2), we get,

x + (3x) + (2x - 10) = 92
    x + 3x + 2x - 10 = 92
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                         6x = 92 + 10
                           x = 102 / 6
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Now,
substituting the value of "x" in equation (1)
 y = 3 (17)
y = 51

Now,
Substituting the value of "x" in equation (2),

z = 2 (17 ) - 10
z = 34 - 10
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So, the numbers are 17, 51 and 24


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3 years ago
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zimovet [89]

Step-by-step explanation:

Given :

1- cosA = 1/2

or, CosA = 1 -1/2

Therefore ; CosA = 1/2 = b/h

According to the Pythagoras theorem,

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Dahasolnce [82]

Answer:

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Read 2 more answers
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