Test 1 Flashcards
even degree and positive leading coefficient
lim as x –> inf –> inf
lim as x–> -inf –> inf
even degree and negative leading coefficient
lim as x–> inf –> -inf
lim as x –> -inf –> -inf
odd degree and positive leading coefficient
lim as x–> inf –> inf
lim as x–> -inf –> -inf
odd degree and negative leading coefficient
lim as x –> inf –> -inf
lim as x –> -inf –> inf
to find the limits at infinity of rational functions, we will divide every term in the function by the term in the denominator with the
highest power of X
if one limit at infinity exists…
it equals the other limit
Find the limit at infinity by dividing every term by the largest power in the denominator, and then find the limit of the numerator and then denominator. The limit of the numerator over the limit over the denominator equals the ________.
how to find the horizontal asymptote
if x –> inf, we divide by the _____ ______ _____ of e^nx in the denominator
most positive power
if x –> -inf, we divide by the ____ ______ ____ of e^nx in the denominator
most negative power
if there is no “most positive” or “most negative” power in the denominator, we
do not divide, and go straight to observing the limit of the numerator and denominator
to find holes, look for factors in the numerator and denominator that
divide completely out from the denominator
to find vertical asymptotes, look for factors in the denominator that
remain after dividing common factors, and set equal to zero
to find where on a graph it is discontinuous, find the
DOMAIN
domain restrictions:
denominator must not equal
zero
domain restrictions:
the argument of an even root must be
non negative, or greater than or equal to zero
domain restrictions:
the argument of a log must be
positive, or greater than zero
rules for continuity
cut off number =5
1) f(5) exists
2) lim as x–>5 exists
3) lim as x–> 5 equals f(5)
slope of the secant line
difference quotient
average velocity
average rate of change also equals
difference quotient
f(x+h)-f(x)/h
instantaneous rate of change
limit of the slopes of secant lines
limit of the difference quotient
slope of the tangent line
r(100)-r(75)/100-75
average rate of change
slope of the tangent line instantaneous rate of change instantaneous velocity limit of the difference quotient limit of the slopes of secant lines
derivative f’
three ways to say f is non-differentiable at x=a?
corner or cusp, discontinuity, vertical tangent line
