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calc project

Across
Integral of square root of f'(x)²+1
function must be continuous with no sharp corners or vertical asymptotes
value that a function approaches
Are under the curve
the sum of a sequence of numbers
- type of discontinuity where the two-sides limit DNE bc the one-sides límite are not equal
the point where the concavity changes. Second derivative = 0
what derivative rule must be applied? D/dx f(g(x))
a Taylor series centered around 0
if a function is continuous and differentiable on an interval then at some point the instantaneous and average rate of change will be equal (acronym)
the function is defined at the point. the function has a limit from that side at that point. the one-sided limit equals the value of the function at the point.
Derivative of position function
aₙ(x-a)ⁿ.
Down
derivative = 0 or DNE
Function approaches a value
(½)ⁿ
an infinite sum giving the value of a function f(z) in the neighborhood of a point a in terms of the derivatives of the function evaluated at a.
function does not approach a value
a kind of visualization of a differential equation
instantaneous rate of change
Integral of the square root of (dx/dt)²+(dy/dt)²
an approximation of the area under the curve using geometric shapes
when a limit is indeterminate you can use ___ and take the derivative of the numerator and denominator and reevaluate the limit.
what derivative rule must be applied? D/dx f(x)(g(x)
determined by the second derivative, describes the rate of change of the function's derivative
a test for convergence where the function must be decreasing, and the limit = 0
type of discontinuity where an asymptote exists
type of discontinuity where f(x) does not exist
what derivative rule must be applied? d/dx x²
when a continuous function is bounded from [a,b] at some value C has to be between [a,b]