Calculus Exam 1 Flashcards
How do you graphicall verify if an equation is a function
vertical line test
Odd function notation
f(-x)=-f(x)
Power function rule:
even powers have axis symmetry, odd powers have origin symmetry
what is the domain for all polynomials
negative infinity, infinity
how do you determine domain of rational function?
define bottom so that it can’t equal zero
what is the ceiling function
smallest number greater than or equal to x
name all parts in equation:
y=af(b(x+c))+d
a = vertical stretch/compression
f = function
b = horizontal stretch/compression
x = x value
c = horizontal shift
d = vertical shift
what does the tangent line do?
line that best approximates the graph at a point
what is the slope of y=e^x
1
what is the inverse of y=e^x
y=lnx…. (f^-1)
how can you check for a 1:1 function
use horizontal line test
what types of functions have inverses
1:1 functions
what is the domain of an inverse function?
the domain of an inverse is the range of the function
what is the inverse of y=a^x
y=log(a)x
what is the inverse of log(e)x
lnx
unless restricted, trig functions are never..
1:1
what is the domain of tan and sin
-pi/2, pi/2
what is the domain of cos
0, pi
what is the secant line
joining two parts of a curve
instant rate of change is corresponds to..
slope of tangent line
what does a limit describe
how a function behaves near a point
3 steps to proving a limit:
1) start with how far f(x) can be from L (which is the epsilon)
2) manipulate to 0 < |x-3| < delta to form |x-3| < epsilon/3
3) can plug in any epsilon to equation to find delta
what is the limit of sin(theta)/sin as x approaches 0?
1
what must you do to prove limit of tan functions?
sandwich theorem
3 points in continuity test
1) f(c) exists
2) limit of f(c) as x approaches c exists
3) limit of f(x) as x approaches c = f(c)
where are constant functions continuous?
everywhere
where are polynomials continous?
everywhere
intermediate value property
whenever a function takes on 2 values, it also takes on all values in between
1/x has a limit of.. as x approaches infinity
0
how to calculate limit at infinity of rational function
must divide numerator and denominator by highest power of x in the denominator
horizontal asymptotes are associated with …
limit of a function as x approaches infinity
trig limits are different when x is approaching.. vs ..
approaching 0 vs infinity
when must we prove a trig limit using sandwich theorem
limits involving infinity
what is an oblique asymptote
slant line asymptote
vertical asymptotes are associated with..
limit equalling neg/pos infinity
what is indeterminate form
0/0
