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].
1 answer:
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
Answer: D
Step-by-step explanation:
If we substitute -12 into this equation we get:
![-3[-12-8]+1.5](https://tex.z-dn.net/?f=-3%5B-12-8%5D%2B1.5)
![-3[-20]+1.5](https://tex.z-dn.net/?f=-3%5B-20%5D%2B1.5)
Because -20 is in absolute value, we simply just use 20.
Thus,

C = pi*d; solve for d.
Divide both sides of this eqn by pi: C/pi = d (answer)
Answer:
3
Step-by-step explanation:
-4(1/4)(-3)= 3
Mark as brainlist.
Answer:
a=6cm
Step-by-step explanation:
Answer:
84.823
Step-by-step explanation:
volume = 1/3 (pi)(r2)(H)