Multiple choice

If $f(x,y) = (ln \,x^2)(e^{2y})$, what is the approximate value of $f(2, \sqrt{2})$?

  1. 23.45

  2. 24.35

  3. 25.34

  4. 25.43

  5. 27.25
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A Correct answer
Explanation

f(2, sqrt(2)) = (ln(2^2)) * (e^(2 * sqrt(2))) = (ln 4) * (e^(2.828)). ln 4 is approx 1.386. e^2.828 is approx 16.91. 1.386 * 16.91 is approx 23.44.

AI explanation

We substitute the values 2 and the square root of 2 into the function, giving the natural logarithm of 2 squared multiplied by e raised to the power of 2 times the square root of 2. The logarithm of 2 squared is 2 times the logarithm of 2, which is approximately 1.386. The exponent 2 times the square root of 2 is approximately 2.828, and e raised to this power is approximately 16.9. Multiplying 1.386 by 16.9 gives a result of approximately 23.42, which is closest to the stated value.

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