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Level 518

Evaluating Limits Analytically


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limit
The unique value that a function approaches as x-values of the function approach c from the left and right sides
Basic Limits
lim k = k
Scalar Multiple
lim [b f(x)] = bL
Sum or Difference
lim [f(x) +/- g(x)] = L+/- K
product
the answer to a multiplication problem
quotient
the answer to a division problem
power
a number produced by raising a base to an exponent
Limits of Polynomial and Rational Functions
If p is a polynomial function and c is a real number then
Limit of a Function Involving a Radical
Let n be a positive integer. The following limit is valid for all c if n is odd, and is valid for c > 0 if n is even
Limit of a Composite Function
If f and g are functions such that lim g(x) = L and lim f(x) = f(L),
Squeeze Theorem
If h(x)<_ f(x)<_ g(x) for all ox in an open interval containing c, except possibly at c itself and if lim h(x) = L = lim g(x)