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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 = threexsquared 3 = three 0 = zero sin x = sinx sin 2x = sintwox sin^2 x = sinsquaredx 1/x = oneoverx 1/(x-1) = oneoverxminus1 infinity = infinity

NOTE: 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.

1 2
  3         4        
5 6           7 8
  9       10                    
  11           12                
14       15              
    16 17   18 19  
21         22          
  27           28  

3.The slope of the tangent line is also known as this.
6.Find the antiderivative: y = 0
7.Yes/No: the derivative of the integral of f(x) is simply f(x).
9.(b-a)/2n[f(x0) + 2f(x1) + 2f(x2)...+ f(xn)] is the general formula for which rule.
11.Find dy/dx: y= 4x^3
13.The derivative represents the average ____ of change.
14.Functions that either increase or decrease along its entire domain are called ________.
20.The second derivative of position is this.
21.True/False: Rolles theorum states that the integral of f(x) is equal to the area of f(x) along a specified interval.
22.Yeah/Nope The trapezoidal rule is the exact value for the area under the curve.
23.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
24.If the second derivative is positive along that interval, the graph of the function is always this.
26.Find dy/dx: y = 900000000000000
27.The horizontal asymptote of f(x) is the limit as x approaches what value?
1.You are given dy/dx: What test do you use to find increasing and decreasing intervals of f(x)?
2.Aff/Neg: Reimann sums measure the slope of the tangent line
4.The Integral of a function is equal to its _______ + C.
5.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 ___________.
8.Find dy/dx: ln x
10.A functious is not continous if its left hand limit does not _____ its right hand limit.
12.Find the antiderivative: y = 1
15.Find the area under the curve y = 3x^2 on the interval [-1,1]
16.Yeah/Nope: not every function has an inverse.
17.Find dy/dx: y = 3
18.The antiderivative of cos (3x) is this.
19.The area under the curve for f(x) is found by using this process.
22.Yay/Nay: The mean value theorum states that only monotonic functions have an inverse.
25.If the second derivative is zero the seconcd derivative test _____.
26.find d^2y/dx: y = 3x
28.True/False: the derivative of position is velocity

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