Calculus Volume 1 · 免费预览
极限运算法则
极限可以按代数法则合并，和、积、商、幂与根都可以通过极限运算；这些法则与代入法结合后，无需借助数值表或图像即可求出大多数极限。
1. The basic laws
The basic laws
2. Substitution and its limits
Substitution and its limits
3. Algebraic moves for 0/0
Algebraic moves for 0/0
4. Limits at infinity
Limits at infinity
5. Sum law in action
Given lim x to 2 of f equals 3 and lim x to 2 of g equals 5, what is lim x to 2 of (f + g)?
6. Quotient law condition
The quotient law says lim of f/g equals lim f over lim g under one essential condition. What is it?
7. Factoring a rational limit
What is lim x to 3 of (x^2 - 9)/(x - 3)?
8. Conjugate move
To evaluate lim x to 0 of (sqrt(x+1) - 1)/x, which algebraic step resolves the indeterminate form?
9. Horizontal asymptote by degrees
What is lim x to infinity of (3x^2 + x)/(2x^2 - 5), the horizontal asymptote of the graph?
10. Power law for limits
Given lim x to a of f equals L, what does the power law say about lim x to a of f(x)^n for a positive integer n?
11. Product law value
lim x to 2 of f equals 4 and lim x to 2 of g equals 3. By the product law, what number is lim x to 2 of f times g? Answer with a number.
12. Substitute a polynomial
What is lim x to 1 of (x^2 + 3x)? Answer with a number.
13. Leading term dominance
What is lim x to infinity of 5/x? Answer with a number.
14. Degree comparison
What is lim x to infinity of (2x^3 + 1)/(x^3 - x)? Answer with a number.