End Behavior
The end behavior for -3x2 + 4x +20 as x goes to infinity.
What is negative infinity?
cos(pi/3)
What is 1/2?
lim(x→8) 7+ √(x+1)
What is 10?
These three things must be equal for f to be continuous at x=2
What is lim(x→2+) = lim(x→2-) = f(2)?
lim(x→0) cosx
What is 1?
The right end behavior for x + sin(x)e-5x
What is infinity?
What is the trig value that corresponds to the x-coordinate?
What is cos(theta)?
lim(x→4) (x2-5x+4)/(x2-2x-8)
What is 1/2?
If the limit of f(x) as x approaches 2 is 4, what can you conclude about f(2)?
What is Nothing?
limit as x approaches pi of sin(x)
What is -1?
The left end behavior model for (2x5 + x4 - x2)/(3x5 + 7x + 7)
What is 2/3?
If f(x)≤ g(x) ≤ h(x) for all x≠ c in some interval containing c and if limit as x→ c of f(x) = L = limit as x→ c of h(x), then
What is the limit as x→c of g(x) = L?
lim(x→9) (x - 9) / (√x - 3)
What is 6?
The 4 types of discontinuity
What are Removable, jump, vertical asymptote, and oscillating?
lim(x→0) cos(x)tan(x)/x
What is 1?
The horizontal asymptote for (3x+6x4-9x2+4)/(11+2x-5x4)
What is y = -6/5?
The tangent of what angle is 1?
What is Pi/4 or 5Pi/4?
lim(x→0) [1/(x+3) - 1/3] / x
What is -1/9?
(simplify with LCD for fraction)
The 6 properties (or rules) of limits
What are Sum, Difference, Product, Constant Multiple, Quotient, Power?
lim(x→π) (x)sec(x)
What is -π?
The limit as x goes to negative infinity of f(x) = (sqrt(4x2-3)/x)
What is -2?
The sine of what angle in the fourth quadrant is -1/2
What is 11Pi/6?
lim(x→1) [√(x+3) - 2] / (x-1)
What is 1/4?
(multiply the conjugate)
Name three times when a limit does not exist.
1. f(x) approaches a different number from left and right side of c 2. f(x) increases or decreases without bound 3. f(x) oscillates between two fixed values
lim(x→π/2) cos(x) / (x-π/2)
What is -1?
Use trig identity that cos(x) = sin(π/2 - x)
Should know lim(x→0) sin(x) / x = 1