HP 15c Manual

 Appendix E: A Detailed Look at f 251 
 
Since  you’re  evaluating  this  integral  numerically,  you  might  think (naively 
in  this  case,  as  youll  see)  that  you  should  represent  the  upper  limit  of 
integration by 1099 – which is virtually the largest number you can key into 
the calculator. Try it and see what happens. 
Key in a subroutine that evaluates the function f(x) = xe-x 
Keystrokes Display  
|¥  000- Program mode. 
´ b 1 001-42,21,  1  
“  002-    1   6  
 003-       12  
* 004-...

252 Appendix E: A Detailed Look at f 
 
The  graph is a  spike  very close  to the origin. (Actually, to illustrate f(x) the 
width of the spike has been considerably exaggerated. Shown in actual scale 
over  the  interval  of  integration,  the  spike  would  be  indistinguishable  from 
the  vertical  axis  of  the  graph.)  Because  no  sample  point  happened  to 
discover  the  spike,  the  algorithm  assumed  that f(x) was  identically  equal  to 
zero  throughout the  interval  of  integration....

 Appendix E: A Detailed Look at f 253 
 
Note  that  the  rapidity  of  variation  in  the  function  (or  its  low-order 
derivatives)  must be  determined  with respect to  the  width of the  interval  of 
integration.  With  a  given  number  of  sample  points,  a  function f(x) that  has 
three  fluctuations  can  be  better  characterized  by  its  samples  when  these 
variations are spread out over most of the interval of integration than if they 
are  confined  to  only  a  small  fraction  of...

254 Appendix E: A Detailed Look at f 
 
In  many  cases  you  will  be  familiar  enough  with  the  function  you  want  to 
integrate  that  you’ll  know  whether  the function  has  any  quick  wiggles 
relative  to  the  interval  of  integration.  If  youre  not  familiar  with  the 
function,  and  you  have  reason  to  suspect  that  it  may  cause  problems,  you 
can  quickly  plot  a  few  points  by  evaluating  the  function  using  the 
subroutine you wrote for that purpose. 
If  for any...

 Appendix E: A Detailed Look at f 255 
 
Keystrokes Display  
0 v  0.000    00 Keys lower limit into  
Y-register. 
‛ 3 1        03 Keys upper limit into  
X-register. 
´ f 1 1.000    00 Approximation to integral. 
®  1.824   -04 Uncertainty of 
approximation. 
This  is  the  correct  answer,  but  it  took almost  60  seconds.  To  understand 
why,  compare  the  graph  of  the  function  over  the  interval  of  integration, 
which  looks  about  identical  to  that  shown  on  page  252,  to  the...

256 Appendix E: A Detailed Look at f 
 
If  the  interval  of  integration  were  (0,  10)  so  that  the  algorithm  needed  to 
sample  the  function  only  at  values  where  it  was  interesting  but  relatively 
smooth,  the  sample  points  after  the  first  few  iterations  would  contribute  no 
new  information  about  the  behavior  of  the  function.  Therefore,  only  a  few 
iterations  would  be  necessary  before  the  disparity  between  successive 
approximations  became  sufficiently...

 Appendix E: A Detailed Look at f 257 
 
Obtaining the Current Approximation  
to an Integral 
When the  calculation of an integral  is requiring  more  time than  you care to 
wait, you may  want to stop and display the current approximation. You can 
obtain the current approximation, but not its uncertainty. 
Pressing ¦ while  the  HP-15C  is  calculating  an  integral  halts  the 
calculation,  just  as  it  halts  the  execution  of  a  running  program.  When  you 
do so, the  calculator stops at...

258 Appendix E: A Detailed Look at f 
 
 If any other program line is displayed, return to Run mode 
and  single-step  (Â)  through  the  program  until  you 
reach  a n instruction  (keycode  43  32)  or  line  000  (if 
there is no n). (Be sure  to  hold  the  key  down 
long  enough  to  view  the  program  line  numbers  and 
keycodes.) 
3. Press | K to view the current approximation. If you want to 
continue  calculating  the  final  approximation,  press − + 
¦.  This  refills  the  stack  with...

 
259 
Appendix F 
Batteries  
Batteries  
The HP-15C is shipped  with two 3 Volt CR2032 Lithium batteries.  Battery 
life depends on how the calculator is used. If the calculator is being used to 
perform operations other than running programs, it uses much less power. 
Low-Power Indication 
A  battery  symbol  ()  shown  in  the  upper-left  corner  of  the  display  when 
the calculator is on signifies that the available battery power is running low. 
When  the  battery  symbol  begins  flashing,...

260 Appendix F: Batteries 
 
To install new batteries, use the following procedure:  
 
 
1. With the calculator turned off, slide the battery cover off. 
2. Remove the old battery.  
3. Insert a new CR2032 lithium battery, making sure that the positive 
sign (+) is facing outward. 
4. Remove and insert the other battery as in steps 2 through 3. Make sure 
that the positive sign (+) on each battery is facing outward. 
5. Replace the battery cover. 
Note: Be  careful  not  to  press  any  keys  while  the...