So apparently Google loves me, and this brings a grand total of 14 invitations they've given me since I started. 6 are sitting here ready to be sent out. Last night's contest was a bit mean, but tonight's could be considered meaner(or nicer, depending on who you are).
Rules are the same generally as last night.6 questions will be posted. When answering a question, please post the number of the question with its answer. Only answer ONE question please. If you don't want Gmail, please don't answer a question to keep it fair. Answers in edited messages will not be accepted, period, to prevent cheating.
Now, on to the torture. These are all selected questions I've plucked from what we could call a "math test." Only final answers will be accepted. Only *exact* answers will be accepted as correct. No approximations.
For these questions, the word "pi" will be used instead of the Greek lowercase letter. Everything else should be in what are generally accepted forms of mathematic notation.
1. A rectangle of length (1/4)pi and height 4 is bisected by the x-axis and is in the first and fourth quadrants, with the leftmost edge on the y-axis. The graph of y=sin(x)+C divides the area of the rectangle in half. What is C?
2. What is the average value of f(x)=3x²-2x on [0,4]?
3. Find the rate of change of f(x)=(x²-4x+3)(x-2) with respect to x at the point (4,6).
4. Find the limit as x approaches 1 of (x-1)/(x³-1).
5. What is (d^2959)/(dx^2959)(-sin(x))?
6. Suppose f(x)=e^(ax)+e^(bx). For how many different pairs (a,b) is f"-2f'-15f=0?
Hopefully I didn't make any errors typing some in. I could've picked a lot harder questions, so don't hate me too much. These were just a lot easier to write since the notation could be done easily in text. Oh, and yes, ALL questions have only one answer to my knowledge.
[This message has been edited by Darth (edited June 19, 2004).]
Rules are the same generally as last night.6 questions will be posted. When answering a question, please post the number of the question with its answer. Only answer ONE question please. If you don't want Gmail, please don't answer a question to keep it fair. Answers in edited messages will not be accepted, period, to prevent cheating.
Now, on to the torture. These are all selected questions I've plucked from what we could call a "math test." Only final answers will be accepted. Only *exact* answers will be accepted as correct. No approximations.
For these questions, the word "pi" will be used instead of the Greek lowercase letter. Everything else should be in what are generally accepted forms of mathematic notation.
1. A rectangle of length (1/4)pi and height 4 is bisected by the x-axis and is in the first and fourth quadrants, with the leftmost edge on the y-axis. The graph of y=sin(x)+C divides the area of the rectangle in half. What is C?
2. What is the average value of f(x)=3x²-2x on [0,4]?
3. Find the rate of change of f(x)=(x²-4x+3)(x-2) with respect to x at the point (4,6).
4. Find the limit as x approaches 1 of (x-1)/(x³-1).
5. What is (d^2959)/(dx^2959)(-sin(x))?
6. Suppose f(x)=e^(ax)+e^(bx). For how many different pairs (a,b) is f"-2f'-15f=0?
Hopefully I didn't make any errors typing some in. I could've picked a lot harder questions, so don't hate me too much. These were just a lot easier to write since the notation could be done easily in text. Oh, and yes, ALL questions have only one answer to my knowledge.
[This message has been edited by Darth (edited June 19, 2004).]
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