Mathematics I (Calculus) - Old Questions

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3. (a) Find the Maclaurin series for e^x and prove that it represents e^x for all x.

4 marks

Asked in 2074

Answer

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Official Answer

Now,

Let d is any positive number with then

So, by Taylor’s inequality

for

Since is a finite value. So

i.e.

for all values of x.

This implies that series converges to e^x for every value of x.