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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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Answer:

Slope=  

2.000

0.800

​  

=0.400

x−intercept=  

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y−intercept=  

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1

​  

=−1.00000

Step-by-step explanation:

STEP

1

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Pulling out like terms

1.1     Pull out like factors :

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Equation at the end of step

1

:

STEP

2

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Equations which are never true

2.1      Solve :    3   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

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Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

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Using equation of motion,

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Hence, this is all for the solution.

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