Name the three conditions under which limits do not exist.
1. f(x) approaches a different number from different sides.
2. f(x) increases or decreases without bound as x approaches c.
3. f(x) oscillates between two fixed values as x approaches c.
100
This value has no meaning as a real number and is referred to as the indeterminate form.
0/0
100
Use the limit process to find the slope of the graph of the function at the specified point.
g(x) = 4/x, (2,2)
-1
100
What is the limit of a function (x is approaching infinity)when the power of the numerator is less than that of the denominator?
0
100
Evaluate the sum on the board by using summation formulas and properties.
44,140
200
Evaluate lim [f(x)+g(x)] given lim f(x)= 3 and g(x)=6.
9
200
Find the limit. lim x→-1 (1-2x-3x^2)/(1+x)
lim=4
200
________ is the study of the rates of change of functions.
Calculus
200
Using the first five terms of the sequence, find the limit of the sequence (if it exists).
a(sub n) = (n+1)!/n!
The limit does not exist.
200
Rewrite the sum on the board as a rational function S(n).
(5n+4)(n+1)/6n^2
300
Find the limit.
lim x→0.5 arcsinx
(the limit of arcsinx as x approaches 0.5)
π/6 or 30◦
300
Evaluate the limit. lim x→16 [4-√(x)]/[x-16]
lim=-0.125 solve by multiplying by the conjugate of the numerator
300
a) Find a formula for the slope of the graph.
b) Use the formula to find the slope at the given point.
g(x) = 1/(x+4), (-2, 0.5)
a) -1/(x+4)^2
b) -1/4
300
Using the first five terms of the sequence, find the limit of the sequence (if it exists).
a(sub n) = [(-1)^n]/n
lim=0
300
Use the limit process to find the area of the region between the graph of the function and the x-axis over the specified interval.
f(x) = 10-x
interval [1, 10]
50 square units
400
Graph f(x)= 2x+1, x<2; x+3 x≥2 and find the limit.
lim=5
400
Find lim h→0 [f(x+h)- f(x)]/h given f(x)= 3x-1
3
400
Find the derivative of the function.
f(x) = 1/(x-9)^1/2
f'(x) = -1/[2(x-9)^3/2]
400
Find the limit of the sequence written on the board.
lim a(sub n)=16/3
400
What is Mr. Trieb's favorite ice cream flavor?
500
What color are Mr. Trieb's eyes?
500
Find lim h→0 [f(x+h)- f(x)]/h given f(x)= 3x-x^2
3-2x
500
a) Find the slope of the graph of f at the given point.
b) Use the result to find an equation of the tangent line to the graph at the given point.
f(x) = x^2 - 1, (2, 3)
a) 4
b) y = 4x-5
500
If Mr. Trieb could have any superhero power, what power would he choose?
What is ....
500
Use the limit process to find the area of the region between the graph of the function and the x-axis over the specified interval.
f(x) = x^2+4
interval [-1,2]