HP 15c Scientific Keystrokes Display Return approximation to, ´ Clear u Hold, ´ f ´ Clear u hold

Appendix E: A Detailed Look at f 243

The uncertainty indicates that the displayed digits of the approximation might not include any digits that could be considered accurate. Actually, this approximation is more accurate than its uncertainty indicates.

Keystrokes	Display
®	7.79	-03Return approximation to
		display.

´CLEAR u

(hold)	7785820888 All 10 digits	of i 2
	approximation.

The actual value of this integral, correct to five significant digits, is 7.7805×10-3. Therefore, the error in this approximation is about (7.7858 − 7.7805)×10-3= 5.3×10-6.This error is considerably less than the uncertainty, 1.45×10-3The uncertainty is only an upper bound on the error in the approximation; the actual error will generally be smaller.

Now calculate the integral in i 3 and compare the accuracy of the resulting approximation to that of the i2 approximation.

Keystrokes ´ i 3

) )

Display

7.786 –03Changes display format to i3.

3.142 00 Rolls down stack until upper limit appears in X- register.

´ f 0

®

®

´CLEAR u (hold)

7.786 –03

1.448 –04

7.786 –03

7785820888

Integral approximated in

i3

Uncertainty of i3 approximation.

Returns approximation to display.

All 10 digits of i 3 approximation.