Approaching Without Ever Getting There
Change this Instant!
What's under my function?
The Endless Journey
Significant Figures
100
A function has a two-sided limit at a point if and only if these two values are equal.
What are the left-hand limit and the right-hand limit?
100
The derivative of a function at a point gives the slope of this at that point.
What is the tangent line?
100
The integral of a function from x=a to x=b is defined as the area bounded by the function and this.
What is the x-axis?
100
The sum of a convergent geometric series with leading term a.
a/(1-r)
100
The father of calculus.
Who is Isaac Newton?
200
The existence of a limit at a point guarantees that the function behaves predictably near that point, but it does not guarantee this property.
What is continuity?
200
For a function to be differentiable at a point, it must also be this.
What is continuous at that point?
200
A left Riemann Sum used to approximate the value of a definite integral will overestimate the true feeling if the function is this
What is decreasing?
200
The conditions for a valid integral test.
What are decreasing, positive and continuous?
200
He likes to approximate solutions to differential equations.
Who is Euler?
300
A function can have an infinite limit at a finite value of x, meaning the function exhibits this type of behavior at that point.
What is a vertical asymptote?
300
A function f has a critical point at x=c and its second derivative at c is negative. Then at x=c, the graph of f has this feature.
What is a maximum?
300
The process of rewriting a rational function of polynomials into a sum and/or difference of the linear factors of its denominator.
What is partial fraction decomposition?
300
f^((n))(0)/(n!)
What is the coefficient of a Maclaurin Series?
300
He doesn't know the meaning of indeterminate.
Who is l'Hopital?
400
A function has a finite left-hand limit and a finite right-hand limit at x = c, but they are not equal. What type of discontinuity does this create, and how does it appear on the graph?
What is a jump discontinuity?
400
The derivative at x=0.
What is undefined?
400
LIATE
What is an acronym used to remember the order of the types of functions used to choose 'u' while using integration by parts? Log, Inverse Trig, Algebraic, Trig, Exp
400
sum_(n=0)^infty ((-1)^nx^(2n+1))/((2n+1)!)
What is sinx ?
400
Always looking at the worst-case scenario.
Who is Lagrange?
500
The Intermediate Value Theorem guarantees that there is at least one value c in (a,b) such that f(c)=0 provided that this is true.
What is f is continuous and f(a) and f(b) are different signs?
500
The conditions needed to apply the Mean Value Theorem.
What are continuous on a closed interval, and differentiable on an open interval?
500
The value of p if the integral converges.
int_1^infty 1/x^p dx
What is p>1?
500
The series ∑ a_n converges, but the series ∑ |a_n| diverges.
What is conditionally convergent?
500
Likes to approximate, but won't move off of zero.
Who is Maclaurin?