The approximate value of $ e^{1.002}$, if $e=2.7183$ is
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2.7237
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2.2737
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2.3772
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2.7273
Reveal answer
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Correct answer
Explanation
e^x is approximately 1 + x + x^2/2. e^1.002 = e^1 * e^0.002. Using e^0.002 approx 1 + 0.002 = 1.002. Result = 2.7183 * 1.002 = 2.7237366.
AI explanation
Using the derivative approximation for exponential functions, e raised to the power of x plus delta x is approximately e raised to the power of x plus delta x times e raised to the power of x. Here x is 1 and delta x is 0.002, so we calculate 2.7183 plus 0.002 times 2.7183. Multiplying 2.7183 by 0.002 gives 0.0054366, and adding this to 2.7183 yields 2.7237.