Analyzing limits involves several methods including numerical and algebraic approaches. Numerically, one can determine limits by examining a table of values to see how a function behaves as it approaches a specific point.
the value that a function or sequence "approaches" as the input or index approaches some value
LIMITS AT INFINITY
Vertical asymptote is any value that makes the denomintaor Limf(x) x= negative or positive infinite be zero.
NUMERICALLY
Find limits numerically by analyzing a table of values.
CONTINUITY
Jump discontinuities occur where the graph has a break in it as this graph does. The function is continuous at this point since the function and limit have the same value. The function is not continuous at this point.
INFINITE
are those that have a value of ±∞, where the function grows without bound as it approaches some value a. For f(x), as x approaches a, the infinite limit is shown as . If a function has an infinite limit at , it has a vertical asymptote there.
ALGEBRAICALLY
Find the limit algebraically by plugging in the x value, factoring, rationalizing the numerator, and finding the lowest common denominator.
