Limits Flashcards

1
Q

What does a limit describe?

A

The f(x) value that a function appoaches at its x value approaches a certain number.

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2
Q

What is a left-hand limit?

A

The limit of a function as it approaches a number from the left (from negative infinity).

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3
Q

What is a right-hand limit?

A

The limit of a function as it approaches a number from the right (from positive infinity).

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4
Q

What criteria must exist for a limit to exist?

A
  • The left-hand limit must exist
  • The right-hand limit must exist
  • These two limits must be equal
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5
Q

lim x–> a (f(x) ± g(x)) = ?

A

lim x–>a (f(x)) ± lim x–>a (g(x))

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6
Q

lim x–>a (f(x) · g(x)) = ?

A

lim x–>a (f(x)) · lim x–>a (g(x))

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7
Q

lim x–>a (c · f(x)) = ?

A

c · lim x–>a (f(x))

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8
Q

lim x–>a (f(x)/g(x)) = ?

A

[lim x–>a f(x)]/[lim x–>a g(x)] if lim x–>a g(x) ≠ 0

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9
Q

If a function f is discontinuous on a point a, does lim x–>a f(x) exist?

A

No

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10
Q

What functions are continuous everywhere in their domains?

A

Polynomials, exponential, logarithmic, sin, cos, sin^-1, cos^-1, and root functions

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11
Q

For functions that are continuous everywhere, how do you find the limit at x = a?

A

Plug a in for x and solve.

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12
Q

What can we say about a function at point x = a if lim x–>a f(x) = f(a)?

A

The function is continuous at a

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