Let f(x) = x^100 e^-x (A) Find a lower bound for f(x) for x > 0. In other words, find a number m such that m < f(x) for all x > 0. Is your choice for m as large as possible? Comment. (B) Based on a and the interval(s) for when f(x) is decreasing, what do you suspect about the limit of f(x) as x approaches infinity?
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Let f(x) = x^100 e^-x
(A) Find a lower bound for f(x) for x > 0. In other words, find a number m such that m < f(x) for all x > 0. Is your choice for m as large as possible? Comment.
(B) Based on a and the interval(s) for when f(x) is decreasing, what do you suspect about the limit of f(x) as x approaches infinity?
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