Limits Flashcards
What does a limit describe?
The f(x) value that a function appoaches at its x value approaches a certain number.
What is a left-hand limit?
The limit of a function as it approaches a number from the left (from negative infinity).
What is a right-hand limit?
The limit of a function as it approaches a number from the right (from positive infinity).
What criteria must exist for a limit to exist?
- The left-hand limit must exist
- The right-hand limit must exist
- These two limits must be equal
lim x–> a (f(x) ± g(x)) = ?
lim x–>a (f(x)) ± lim x–>a (g(x))
lim x–>a (f(x) · g(x)) = ?
lim x–>a (f(x)) · lim x–>a (g(x))
lim x–>a (c · f(x)) = ?
c · lim x–>a (f(x))
lim x–>a (f(x)/g(x)) = ?
[lim x–>a f(x)]/[lim x–>a g(x)] if lim x–>a g(x) ≠ 0
If a function f is discontinuous on a point a, does lim x–>a f(x) exist?
No
What functions are continuous everywhere in their domains?
Polynomials, exponential, logarithmic, sin, cos, sin^-1, cos^-1, and root functions
For functions that are continuous everywhere, how do you find the limit at x = a?
Plug a in for x and solve.
What can we say about a function at point x = a if lim x–>a f(x) = f(a)?
The function is continuous at a