AP Calculus Vocabulary Flashcards
discontinuity or jump
the x-value at which a limit will not exist due to a sudden change in y-value
limit
a y-value that a function approaches as x-values get closer and closer to a specified number
infinity
what a limit approaches as it gets closer to an asymptote, or the behavior of a rational function as x approaches infinity and the power on top is larger than the power on the bottom
removable
type of discontinuity that is usually characterized by a hole in the graph
zero
the behavior of a rational function as x approaches infinity if the power on bottom is larger than the power on top
one-sided limit
a limit that only takes into account what y-value is being approached from one side of the function (susually denoted by a plus or minus)
quotient rule
d/dx(u/v)=vu’-uv’/v^2
derivative of e^x
e^x
chain rule
d/dx(f(g(x)))=f’(g(x))*g’(x)
derivative of sin(x)
cos(x)
power rule
d/dx(u^n)=nu^n-1
derivative of ln(x)
1/x
derivative
formal name for the instantaneous rate of change or slope of the tangent line
product rule
d/dx(uv)=uv’+vu’
derivative of log(a)x
1/x(ln(a))
derivative of cos(x)
-sin(x)
velocity
the first derivative of position or the anti-derivative of acceleration
slope of a tangent line
found by taking the derivative and plugging in a specified x-value
equation of a tangent line
y-y1=m(x-x1)
position
generally a function given that determines where something is at a given time or the anti-derivative of velocity
acceleration
the second derivative of position
jerk
the third derivative of position
implicit differentiation
taking the derivative of an equation that has x’s and y’s intermixed
optimization
process by which we use the derivative to maximize or minimize a given function
grpahical analysis
the use of the original function and it’s first and second derivatives to determine the graphical behaviors of a given function
maximum
what occurs when the first derivative is equal to zero or is undefined and also changes from positive to negative
minimum
what occurs when the first derivative is equal to zero or is undefined and also changes from negative to positive
critical point
where the first derivative is either equal to zero or undefined
concave up
what occurs on a graph of the original function when the second derivative is positive
concave down
what occurs on a graph of the original function when the second derivative is negative
point of inflection
f’(c)=f(b)-f(a)/b-a on [b,a] if the function is continuous and differentiable
mean value theorem
where the second derivative is equal to zero or is undefined
anti-derivative
what one takes the derivative of to arrive at a given function
initial value problem
solving for c when given a derivative and a point that exists on the original graph
constant
what must be added on to the end of an anti-derivative in order to consider all cases of that anti-derivative
u-substitution
what can be used to integrate something that appears to be a chain rule of some sort
slope field
what is used to get an idea of what the original function may look like based on the derivative and slopes at particular points
LRAM
estimating area between the curve and the x-axis using rectangles and using the left hand side of the subinterval to determine the height of the rectangle
RRAM
estimating area using rectangles and using the right hand side of the subinterval to determine the height of the rectangle
MRAM
estimating area using rectangles and using the middle of the suinterval to determine the height of the rectangle
reimann sum
using rectangles that are not measured in equal subintervals to estimate the area between a curve and the x-axis
pi*r^2
area of a circle
1/2bh
area of a triangle
b^2
area of a square
integral
? function dx
limits
from where to where (function values) an integral is evaluated
dx
what is included on the end of an integral to let one know that the integral is taken with respect to x
fundamental theorem of calculus part 1
d/dx?a-x f’(x) dt= f(x)
fundamental theorem of calculus part 2
?a-b f(x) dx = F(a)-F(b) if f(x) is continuous on [a,b]
definite integral
the sign that is used to indicate finding the area that exists between the curve and the x-axis
area between two curves
found by ?a-b top-bottom dx
accumulation
when areas between the curve and the x-axis represent a gathering of something (like distance traveled)
net change
?a-b(function adding something) dt - ?a-b (function subtracting something) dt
average rate of change when given a rate
1/a-b ?a-b f(x) dx
L’Hopitals rule
procedure by which one can take the limit of a function that was previously thought to be indeterminant
cross sections
what we use to find the volume generated by using shapes that span a base with two functions
disk method
the process of revolving the area of one function around the x-axis
washer method
the process of revolving the area of two functions around the x-axis
revolving around x-axis
?a-b pi(furthest^2-closest^2) dx
revolving around y-axis
?a-b pi(furthest^2-closest^2) dy
revolving around other axes
process by which we move an area to revlove around an axis by shifting them up, down, left, or right to find the voulme generated by revolving said areas
