Question

Evaluate the Limit lim x→[infinity] as from the right of (250 - eˣ)

a) 250
b) -[infinity]
c) [infinity]
d) 0

Answer 1

The limit of the function (250 - e^x) as x approaches infinity is -infinity because the exponential term e^x grows much faster than the constant term 250, making the expression increasingly negative. The correct answer is b) -infinity.

Step-by-step explanation:

The student is asking to evaluate the limit of the function (250 - ex) as x approaches infinity from the right. In this context, 'from the right' means that the x values are becoming larger and larger. As x grows without bound, the exponential term ex increases at a much faster rate than any linear term, such as 250.

When evaluating the limit lim x→∞ (250 - ex), we notice that ex goes to infinity, hence the (250 - ex) part will become more and more negative. Therefore, the limit of this expression as x approaches infinity is -infinity.

This means the correct answer is b) -infinity.