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Calculus Puzzle

Achuta Kadambi

This puzzle has simple problems, theorums, and properties that are an integral part (no pun intended) of calculus. A few words on notation.3x^2 = threexsquared3 = three0 = zerosin x = sinxsin 2x = sintwoxsin^2 x = sinsquaredx1/x = oneoverx1/(x-1) = oneoverxminus1infinity = infinityNOTE: For all indefinite integrals, forget about the C. NOTE: For all true/false questions, I changed the wording a bit. I will give you a positive/negative expression: IE: True/False, Yeah/Nope, Yay/Nay, and you have to pick the correct one.

infinity Find the antiderivative: y = 1
concaveup True/False: Rolles theorum states that the integral of f(x) is equal to the area of f(x) along a specified interval.
nope True/False: the derivative of position is velocity
true Yes/No: the derivative of the integral of f(x) is simply f(x).
integration Yeah/Nope: not every function has an inverse.
x If the second derivative is positive along that interval, the graph of the function is always this.
derivative Find the area under the curve y = 3x^2 on the interval [-1,1]
monotonic The slope of the tangent line is also known as this.
twelvexsquared The horizontal asymptote of f(x) is the limit as x approaches what value?
no Find dy/dx: ln x
two The antiderivative of cos (3x) is this.
acceleration Find dy/dx: y = 3
antiderivative When the first derivative is negative at the left of the critical point and positive at the right of the critical point, the critical point is a relative ___________.
firstderivativetest Yay/Nay: The mean value theorum states that only monotonic functions have an inverse.
zero The second derivative of position is this.
equal The derivative represents the average ____ of change.
rate The area under the curve for f(x) is found by using this process.
sinthreex You are given dy/dx: What test do you use to find increasing and decreasing intervals of f(x)?
zero Find dy/dx: y= 4x^3
nay Yeah/Nope The trapezoidal rule is the exact value for the area under the curve.
false Aff/Neg: Reimann sums measure the slope of the tangent line
yeah Functions that either increase or decrease along its entire domain are called ________.
zero Find the antiderivative: y = 0
aff Aff/Neg: The limit definition to find area using "n" subintervals, as n approaches infinity, is an accurate measure of the area under the curve on a specified interval
oneoverx If the second derivative is zero the seconcd derivative test _____.
minimum The Integral of a function is equal to its _______ C.
neg (b-a)/2n[f(x0) 2f(x1) 2f(x2)... f(xn)] is the general formula for which rule.
zero find d^2y/dx: y = 3x
fails A functious is not continous if its left hand limit does not _____ its right hand limit.
trapezoidalrule Find dy/dx: y = 900000000000000

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