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    Find Exponential Equation from data points

    ... and a few seconds after I posted this, I realized that we're using the wrong variable. X instead of t, and it works. Rage! Rage factorial
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    Find Exponential Equation from data points

    Hi guys I'm helping my girlfriend with her Calc 1 homework and we seem to be stuck on this one problem. Am I missing something obvious? Homework Statement Homework Equations P = P_0 a^t \frac{5}{20} = \frac{P_0 a^1}{P_0 a^{-1}} \frac{1}{4} = a^2 a =...
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    Evaluating a Series

    Homework Statement First, I'd like to thank everybody a head of time. You guys have been an enormous help. Second, I don't mind telling you that I'm finding sequences and series extremely frustrating. I usually pick this stuff up like nobody's business. My problem is attached, but I will copy...
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    Approximations rules of a function

    It took some mathematical gymnastics, but I eventually got the right number. I'm running into a strange problem with these rules. I don't seem to need to multiply by dx for some reason I can't fathom.
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    Approximations rules of a function

    I think you were absolutely right, Mark but I plugged this in but I'm getting something just above 0.3, which is way too low.
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    Approximations rules of a function

    Thanks, Mark44. I must have transcribed my trapezoid rule incorrectly. Thanks for the clarification on my midpoint rule. I'm gonna give that a try!
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    Approximations rules of a function

    Homework Statement Given the following integral and value of n, approximate the integral using the methods indicated (round your answers to six decimal places): \int_0^1 e^{-3x^2} dx n = 4 (a) Trapezoidal Rule (b) Midpoint Rule This is the only one I'm having trouble...
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    Average Velocity and Average Speed of Integral

    I should have had that on the top of my head! Duh!
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    Find the integral of annoying

    Welcome to the wonderful world of integrals! There are times when I want to kick small, defenseless animals because of this stuff. I usually listen to some thrash metal while studying math. I don't know why, but it helps! Try to remember as many identities as you possibly can. It makes life a...
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    Average Velocity and Average Speed of Integral

    Homework Statement An object moves with velocity v(t) = −t2 +1 feet per second between t = 0 and t = 2. Find the average velocity and the average speed of the object between t = 0 and t = 2 Homework Equations \frac{1}{b-a} \int_a^b f'(x) dx avg value of a function The Attempt...
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    Volume of a boat problem

    Agreed. Tip of the hat to Mark44!
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    Volume of a boat problem

    lol, I forgot the units and the 10,000. Thanks a ton! You've been a great help.
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    Volume of a boat problem

    So now I'm finishing the evaluation: Original: V = 2L [Hx - \frac{a}{3} x^3]^{\sqrt(\frac{H}{a})}_0 V = 2L [H{\sqrt(\frac{H}{a})} - \frac{a}{3} {\sqrt(\frac{H}{a})}^3] V = 2L [H{\sqrt(\frac{H}{a})} - \frac{a}{3} \frac{H}{a} {\sqrt(\frac{H}{a})}] V = 2L...
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    Volume of a boat problem

    I don't see where L and H are specified. The only information that it gives you is that 1 m3 of water is 10000 newtons. L and H are constants, but they're not specified. As far as I can tell, H is where y = (a constant) and provide the upper limit of the the top of the boat, but is not...
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    Volume of a boat problem

    Homework Statement The design of boats is based on Archimedes' Principle, which states that the buoyant force on an object in water is equal to the weight of the water displaced. Suppose you want to build a sailboat whose hull is parabolic with cross section y=ax2, where a is a constant. Your...
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    Area between two graphs

    Homework Statement Find the area of the region enclosed between y=4sin(x) and y=2cos(x) from x=0 to x=0.8pi. Homework Equations \int^{0.8\pi}_0 dx g(x) = 4\sin(x) f(x) = 2\cos(x) The Attempt at a Solution This problem needs to be split up into two parts...
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    Riemann Sum from Indefinite Integral

    You're right! I can't believe I forgot this. Thanks dynamicsolo! btw, That's some great advice in your signature. For future reference, \sum_i^4 \frac{3}{x} + 2 \rightarrow Right (i)(\frac{n}{7-3})[f(3) + f(4) + f(5) + f(6)] Left (i)(\frac{n}{7-3})[f(7) + f(4) + f(5) + f(6)]
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    Difficult Indefinite Integral (substitution problem?)

    gb7nash, I went back and fixed that problem. Hey guys, thanks to all of you! You've been a great help.
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    Difficult Indefinite Integral (substitution problem?)

    I ended up going, u = x + 8 x = u - 8 \int [u-8]/[sqrt(u)] du \int (u-8)u^{-1/2} du \int u^{1/2} - 8u^{-1/2} du = c + \frac{2}{3} u^{3/2} - 16 u^{1/2} c + \frac{2}{3} (8+x)^{3/2} - 16 (8+x)^{1/2} Thanks everybody!
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    Behind on Trig Identities

    Agreed, my method was the memorize the big three and manipulate them.
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    Difficult Indefinite Integral (substitution problem?)

    u = \sqrt{x+8} \rightarrow du = (1) \frac{1}{2 \sqrt{x+8}} dx I don't think that helps... u = x+8 \rightarrow du = 1 dx I don't think that helps, either. Am I missing something obvious?
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    Behind on Trig Identities

    I made flashcards, but I agree that you need to practice them with problems. Here are a few of mine: \sin ^2 x + \cos ^2 x = 1 1 - \sin ^2 x = \cos ^2 x 1 - \cos ^2 x = \sin ^2 x \sec ^2 x - \tan ^2 x = 1 \sec ^2 x - 1 = \tan ^2 x \sec ^2 x = 1 + \tan ^2...
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    Difficult Indefinite Integral (substitution problem?)

    Homework Statement \int (\frac{x}{\sqrt{x+8}}) dx The Attempt at a Solution I gotta be honest, I don't even really know where to start with this problem. So bear with me as I take a wild stab in the dark. This section was substitution problems, ... \frac{x}{\sqrt{x+8}} = \sqrt{...
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    Riemann Sum from Indefinite Integral

    Homework Statement Consider the integral, \int _3 ^7 (\frac{3}{x} + 2) dx a) Find the Riemann Sum for this integral using right endpoints and n=4. b) Find the Riemann Sum for this integral using left endpoints and n=4. Homework Equations The sum, \sum^{n = 4} (\frac{3}{x} + 2) The graph...
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