Limits & Derivatives
Applications of Derivatives
Integrals
Applications of Integrals
Sequences & Series
Math Trivia
100
This is the slope of the tangent line to f(x) = \frac{2}{3}\sqrt{x} - x
What is -\frac{5}{6} ?
100
This is the largest critical value of y = -x^3 + 2x^2 + 2 .
What is \frac{4}{3} ?
100
Given F(3) = 1 and F(-1) = 2 , this is the value of \int_{-1}^3 F'(x) \ dx .
What is -1 ?
100
This gives the area between the graph of y = 4/{x^2} , the x -axis, and the lines x = -2 and x = -1 .
What is 2?
100
The n th term of the sequence a_n = (\frac{3}{4})^{n - 1} approaches this value.
What is 0?
100
This famous English mathematician is often credited as the inventor of calculus also had a deep interest in alchemy, spending many years of his life conducting secret experiments in the hope of discovering the fabled Philosopher’s Stone.
Who is Sir Isaac Newton?
200
The value of a+b that makes f continuous.
f(x) = {(x + 4, x \leq 1),(ax^2 + bx, x > 1):}
What is 5?
200
This theorem states that, for a differentiable function, there is at least one value of x for which the function's average rate of change is equal to its instantaneous rate of change.
What is the Mean Value Theorem?
200
This integration technique would be used to evaluate \int x^5 \ln(3x) \ dx .
What is integration by parts?
200
This method of finding the volume of a solid of revolution is used when there is a gap between the region being revolved and the axis of revolution.
What is the washer method?
200
These three characteristics are true of a function f(n) = a_n that can be applied to an Integral Test for \sum_{n = 1}^{\infty} a_n .
What is that f is positive, continuous, and decreasing on [1, \infty) ?
200
Also known as Leonardo of Pisa, this famous Italian mathematician is best known for discovering a sequence where each number is the sum of the two previous numbers.
Who is Fibonacci?
300
This is the value of h'(2) given h(x) = [f(x)]^2.
What is -8 ?
300
This is the minimum value of f(x) = x^3 + 6x^2 + 9x + 3 on the interval [-4, 0] .
What is -1 ?
300
This is the derivative of F(x) = \int_3^{2x} \cos(t^2) \ dt with respect to x .
What is 2\cos(4x^2) ?
300
This is the particular solution to the initial-value problem below.
\frac{dy}{dx} = xy^2, \ y(2) = -2/5
What is y = -\frac{2}{x^2 + 1} ?
300
The infinite series below converges to this.
1 - \frac{(\pi/2)^2}{2!} + \frac{(\pi/2)^4}{4!} - \ldots
What is 0?
300
This mathematical property of numbers states that the order of the terms when performing addition or multiplication does not affect the end result.
What is the commutative property?
400
This is the derivative of 5x^3 = -3xy + 2 with respect to x .
What is \frac{-y-5x^2}{x} ?
400
The Second Derivative Test states that a function f has a relative maximum at x = c under these two conditions.
What is f'(c) = 0 and f''(c) < 0 ?
400
This is the antiderivative of
f(x) = \frac{2x + 3}{x^2 + 3x + 4}
What is ln|x^2 + 3x + 4| + C ?
400
This is the area between the curves y = 2x^{2/3} and y = x .
What is \frac{32}{5} ?
400
The series below converges to this value.
\sum_{n = 0}^{\infty} \frac{2^{n - 1}}{3^n}
What is 3/2 ?
400
This branch of mathematics is the study of counting things.
What is combinatorics?
500
This is the value of the limit below.
\lim_{h \to 0} \frac{(1 + h)^98 - 1}{h}
What is 98?
500
This is the value of the limit below.
\lim_{x \to 0} \frac{e^x - e^{-x}}{x}
What is 2?
500
This kind of Riemann sum would underestimate the true value of an increasing function.
What is a left Riemann sum?
500
This gives the average value of f(x) = -3\sqrt{2x - 6} on the interval [3, 5] .
What is -4 ?
500
This mathematician, often confused with an NBA basketball player, developed an error bound for Taylor and Maclaurin polynomials.
Who is Lagrange?
500
Rounded off after two decimal places, the Golden Ratio (φ) is often approximated as this number.
What is 1.62?