Flashcards in 2.1.4 The Limit Laws, Part I Deck (7):
- Since limits are just numbers, a lot of the properties of real numbers also apply to limits.
- Taking the limit of a function is an operation, but the resulting limit is just a number. Therefore, it makes sense that limits have a lot of the same properties that numbers do.
- The limit of a sum of two functions is equal to the sum of the limits.
- The limit of a difference of two functions is equal to the difference of the limits.
- The limit of a product of two functions is equal to the product of the limits.
- The limit of a quotient of two functions is equal to the quotient of the limits, provided that the denominator does not equal zero.
- The limit of a function multiplied by a constant is equal to the constant multiplied by the limit.
In addition, the limit of a function raised to a power is equal to the limit raised to that power.
Suppose you are told that lim x→1 f(x)=3 and lim x→1 g(x)=−1. What is the value of lim x→1 [f(x)+2g(x)]?
Given lim x→cf(x)=2 and lim x→cg(x)=4, evaluate lim x→c[2f(x)−g(x)].
Given lim x→ 4 f(x)=2 and lim x→ 4 g(x)=3,evaluate lim x→ 2 [f(x)−g(x)/2f(x)].
The limit cannot be determined from the information given.
Is the following equation true for all values of x, a, and c ? limx→ a [c⋅f(x)+g(x)]=c[limx→ af(x)+g(x)]
Given lim x→2f(x)=3 and lim x→2g(x)=2,evaluate lim x→23f(x)−g(x)/g(x).