Final exam Flashcards
2.1
average velocity
change in distance/ change in time
2.1
instantaneous velocity
1st derivative of a position equation
acceleration
2nd derivative of position function
2.1
slope using two points
Y2-Y1/X2-X1
Point slope form
(Y-Y1)=m(X-X1)
2.2
If a limit as X approaches 3+ = 4 and the limit as X approaches 3- = -4 does the limit exist?
no the limit does not exist, must agree on both sides
definition of a vertical asymptote
limit as x approaches a of f(x) = positive or negative infinity
a non zero number/ 0 =
+- infinity
2.5
what are the three points needed for a function to be continunous?
- f(a) is defined
- limit as x approaches a = f(a)
- the limit as x approaches a exsits (cant be one sided)
domain of polynomials
All reals
domain of a rational function
where the denominator does not = 0
domain of trig functions
all reals
domain of exponential functions
ex: e^x, 2^x, 7^x
all reals
domain of logarithmic functions
ex: ln, log
(0, infinity)
2.5
Intermediate value theorum
on a closed interal from [a,b] a continuous function will have a value for f(c) somewhere bc/ it is continuous
domain of odd and even root functions
odd (all reals)
even [o, infinity)
2.7
definition of a derivative
- lim as h approaches 0 f(a+h) -f(a)/h = f(x)-f(a)/x-a
- the slope of the tangent line
2.8
What does it mean to be differentiable?
if a function is differentibale at a point that means the derivative exists there and it is continuous
not differentiable where the derivative cannot exist
2.8
True or false? if x= a is cont then f is differentiable at x=a
false, you cant swap the sentence and still have it be true
3.1
derivative of b^x=
b^x *ln(b)
3.5
Implicit differentation
taking the derivative on both sides with the assumption that y is a function/ y= f(x)
3.10
differentials
dy=fâ(x)* dx
use this for measurement error problems
3.10
surface area of a cube
6a^2
4.1
extreme value therorum
if f(x) is continous on a closed interval then f(x0 has an absolute max and min on that interval
on closed intervals you can choose the ends