Taylor series for e^x with loop

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Allison 2022-7-18

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编辑： Torsten 2022-7-19

How would I solve this problem and only compute the first 12 interations?

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John D'Errico 2022-7-18

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Lacking any code shown before, there was no evidence that you had done anything, on clear homework. But now you have shown at least some effort.

Note that I edited your code to make it readable. You might want to learn to do that, using the buttons on top of the edit window in Answers.

My questions would be:

1. What do you think this

index=1:n;

line does?

Does it serve any purpose, since index is never used?

2. Is n ever changing? How about the variable i? So will your loop ever terminate?

3. Since you will be generating a loop that explicitly goes for ALWAYS exactly 12 iterations, would a for loop be a better choice than a while loop?

4. What does this line do, since that is not the general series for exp(x)?

ex= 1+x+((x)^i/factorial(i));

(Yes, it is sort of related, in the sense that the first two terms are correct, and the third term there you have written is a form for the general term in the sum. But that does not make it the correct sum.)

5. What are you doing with the variable ex? Did not the series involve a sum, in this case of 12 total terms?

6. Is the fprintf syntax correct? Did you read the help for fprintf? Why not? Look at the examples shown in the docs for fprintf.

Why not take another shot at it, based on the comments I've made here.

Allison 2022-7-19

My bad I should've taken more time to think through the problem does this seem on the right track?

Torsten 2022-7-19

编辑：Torsten 2022-7-19

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Works, I guess.

%x = input('Enter value of x');
x = 2;
value=0;
for i=0:12
    value = value + x^i/factorial(i);
end 
fprintf('Computed Value: %f', value)
Computed Value: 7.389055
value
value = 7.3891
exp(2)
ans = 7.3891

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Answer 1

Lateef Adewale Kareem 2022-7-19

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%% This is more efficient
x = 2;
v = 1;
n = 1;
d = 1;
for i = 1:20
    n = n*x;
    d = d*i;
    v = v + n/d;
end
fprintf('Computed Value: %f', v)
Computed Value: 7.389056

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Torsten 2022-7-19

编辑：Torsten 2022-7-19

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x = 2;
v = 1;
s = 1;
for i = 1:20
    s = s * x/i;
    v = v + s;
end
fprintf('Computed Value: %f', v)
Computed Value: 7.389056

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Taylor series for e^x with loop

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Taylor series for e^x with loop

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