Determine the largest interval in which a number x, must lie to approximate V2 withrelative error of at most 107*.Oo <2. < 1.414072 O0 <a < 1.414354© 1.414072 < x, < 1.414354© 1.414354 < ax, < 1.414072

The question seems to be asking for the interval in which a number x must lie to approximate the square root of 2 with a relative error of at most 10^(-7).

The square root of 2 is approximately 1.41421356.

A relative error of 10^(-7) means that the approximation can be off by 0.0000001 times the actual value.

So, we calculate the bounds of the interval as follows:

Lower bound = sqrt(2) - sqrt(2)*10^(-7) = 1.41421356 - 0.000000141421356 = 1.414213418578644

Upper bound = sqrt(2) + sqrt(2)*10^(-7) = 1.41421356 + 0.000000141421356 = 1.414213701421356

So, the number x must lie in the interval (1.414213418578644, 1.414213701421356) to approximate the square root of 2 with a relative error of at most 10^(-7).

Please note that the options provided in the question do not match the calculated interval. There might be a mistake in the question or the options provided.