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无穷、极限与幂函数
当输入无上界增大或函数值无上界增大时，我们如何用极限记号简洁地表达函数的行为？
1. Introduction
Introduction
2. Limit notation
Limit notation
3. Power functions
Power functions
4. Summary
Summary
5. Limit of a decaying exponential
As t grows without bound, e^(-t) approaches what value? Give the integer.
6. Comparing powers on different intervals
For powers x^a and x^b with a < b, where is x^b larger than x^a?
7. Shape trends across the power family
As the exponent n increases in x^n for even n, how does the graph change?
8. Negative exponents on the two intervals
For negative exponents with a < b, such as -3 < -2, how do x^a and x^b compare on x > 1 and on 0 < x < 1?
9. Limit of a reciprocal power
As x grows without bound, 1/x^3 approaches what value? Give the integer.
10. Comparing logarithm, polynomial and exponential growth
Which ordering of growth rates as x grows is correct: ln x, x^2 and e^x?
11. A reciprocal power tends to zero
For every positive integer n, 1/x^n approaches 0 as x grows without bound.