DEFINITION
The value of a function increases without bound.
Positive Infinity
A concept that describes something that is limitless or unbounded.
Infinity
Express what represents the limit of x2 as x approaches 5?
write it on the board
dy/dx (c)=0
Constant Rule
d/dx (x) = x
f'(x) = 1
Means replacing the variables (letters) in an algebraic expression with their numerical values.
Substitution
lim x-->3 (x+2)
Answer: 5
f(x) = -9x2+6x-27 ; x=3
f(3) = 36
d/dx [f(x) x g(x)] = f'(x) + g'(x)
Product Rule
d/dx (10x2 -5) = ?
f'(x) = 20x
A function has an infinite limit at a point a if it either increases or decreases without bound as it approaches a.
Infinite Limit
lim x-->2 (x4 + 3)
Answer: 19
f(x) = 4x2+2x+6 ; x= -6
f(-6) =130
a set of inputs, a set of outputs, and a rule for mapping each input to exactly one output
functions
f(x) = x3 + 4x
f'(x)=3x2 + 4
Which means computing the output [f(a)] by substituting a specific value [a] into the function [f(x)].
Function Evaluation
lim x-->2 [(x2 - 4) / (x-2)]
Answer: 4
lim x --> 2 (2x2 - 8x + 4)
Final Answer: -4
Express Exponential Rule
write it on the board
Chain Rule
Describes how a function behaves as x approaches positive or negative infinity.
End Behavior
lim x-->0 [sqrt(x+1) - 1] / x
Answer:1/2
lim x --> 5 (4x2 + 2x + 6)
Final Answer: 116
d/dx (sin x) = ?
d/dx (sin x) = cos x
d/dx (ln x) = 1/x
Logarithm Rule