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for each a your 4 many terms the do you need to achieve a relative error smaller truncated than 10-8? +15. a Specifically, should implement exp for r +1,+10, function x) Your function er. lim compute built-in to n with in sum Matlab function innite function the r, how of Problem Write version Compare Are the results for 0 different from those for r 0? If so, what is a likely cause for this difference?
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Answer #1

matlab script:

prompt='please enter n value: ';
n=input(prompt);
prompt='please enter x value: ';
x=input(prompt);
sum=0;
for i= 0:n
    sum=sum+x^i/factorial(i);
end
fprintf('value of e^x from series :');
disp(sum);
fprintf('value of e^x from build in function :');
disp(exp(x));

comparision output for given cases:

output:-
>> 10^-8

ans =

1.0000e-008

following differences are nearor to above 10^-8 value


for x=+1 minimun n is 6, for x=-1 minimum n is 7, following is the result
please enter n value: 10
please enter x value: 1
value of e^x from series :    2.7183

value of e^x from build in function :    2.7183

please enter n value: 10
please enter x value: -1
value of e^x from series :    0.3679

value of e^x from build in function :    0.3679

please enter n value: 5
please enter x value: 1
value of e^x from series :    2.7167

value of e^x from build in function :    2.7183

please enter n value: 7
please enter x value: 1
value of e^x from series :    2.7183

value of e^x from build in function :    2.7183

please enter n value: 6
please enter x value: -1
value of e^x from series :    0.3681

value of e^x from build in function :    0.3679

please enter n value: 7
please enter x value: -1
value of e^x from series :    0.3679

value of e^x from build in function :    0.3679


for x=+10 minimun n is 10, for x=-10 minimum n is 35, following is the result
please enter n value: 15
please enter x value: 10
value of e^x from series : 2.0953e+004

value of e^x from build in function : 2.2026e+004

please enter n value: 10
please enter x value: 10
value of e^x from series : 1.2842e+004

value of e^x from build in function : 2.2026e+004

please enter n value: 7
please enter x value: 10
value of e^x from series : 4.8507e+003

value of e^x from build in function : 2.2026e+004

please enter n value: 9
please enter x value: 10
value of e^x from series : 1.0087e+004

value of e^x from build in function : 2.2026e+004

please enter n value: 33
please enter x value: -10
value of e^x from series : 1.9092e-005

value of e^x from build in function : 4.5400e-005

please enter n value: 35
please enter x value: -10
value of e^x from series : 4.3286e-005

value of e^x from build in function : 4.5400e-005

please enter n value: 34
please enter x value: -10
value of e^x from series : 5.2964e-005

value of e^x from build in function : 4.5400e-005


for x=+15 minimun n is 17, for x=-15 minimum n is 52, following is the result
please enter n value: 25
please enter x value: 15
value of e^x from series : 3.2488e+006

value of e^x from build in function : 3.2690e+006

please enter n value: 20
please enter x value: 15
value of e^x from series : 2.9978e+006

value of e^x from build in function : 3.2690e+006

please enter n value: 15
please enter x value: 15
value of e^x from series : 1.8571e+006

value of e^x from build in function : 3.2690e+006

please enter n value: 17
please enter x value: 15
value of e^x from series : 2.4480e+006

value of e^x from build in function : 3.2690e+006

please enter n value: 16
please enter x value: 15
value of e^x from series : 2.1710e+006

value of e^x from build in function : 3.2690e+006

please enter n value: 55
please enter x value: -15
value of e^x from series : 3.0510e-007

value of e^x from build in function : 3.0590e-007

please enter n value: 53
please enter x value: -15
value of e^x from series : 2.9493e-007

value of e^x from build in function : 3.0590e-007

please enter n value: 52
please enter x value: -15
value of e^x from series : 3.4527e-007

value of e^x from build in function : 3.0590e-007

please enter n value: 51
please enter x value: -15
value of e^x from series : 1.6740e-007

value of e^x from build in function : 3.0590e-007

the diferences are vary for the +ve numbers and -ve numbers because in -ve numbers alternative numbers having -ve sign causes substraction insted of summation

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