GATE 2024 AG – Question 47
Approximate $e^{2x}$ at x=1/2 using the first four Taylor terms about 0. Report to three decimals.
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Correct answer: 2.665 to 2.668
Explanation
The first four terms are $1+2x+(2x)^2/2!+(2x)^3/3!$. At x=.5,this is $1+1+1/2+1/6=8/3=2.6666667$,rounded **2.667**. This is the four-term approximation requested, rather than the full exponential value e.