Question

Find approximate value of e^10.1^9.09, given e^90 = 1.22 * 10^39.

(a) 2.41 * 10^39

(b) 2.42 * 10^39

(c) 2.43 * 10^39

(d) 2.44 * 10^39

The question was posed to me in quiz.

My query is from Errors and Approximations topic in chapter Partial Differentiation of Engineering Mathematics

Answer 1

Correct answer is (b) 2.42 * 10^39

For explanation I would say: Let, f(x,y) = e^x^y = e^xy

Now by differentiating,

^∂f⁄∂x = ye^xy and ^∂f⁄∂y = xe^xy

Now, putting, x = 10, y = 9, δx = .01 and δy = .09

We get,

^∂f⁄∂x = 1.09* 10^40 and ^∂f⁄∂y = 1.22* 10^40

Hence, df = 1.27* 10^39

Hence, f(x + δx, y + δy) = e^10.1^9.09 = 2.42 * 10^39.