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  1. S

    Reduction formula integration method help

    It depends on the function it self. Personally, I think integration by parts is the famous way of finding the reduction formulas.
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    Infinite series sin(1/n)/n ?

    You can use the comparison tests since sin(1/n) is positive since the angle (1/n) is in the first quadratic for n=1,2,3,.... To test it, you could use the limit comparison test with a p-series, can you do that ?
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    Test the series for convergence

    I tried that but its not easy to find that f and also f must be positive
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    Test the series for convergence

    Still searching for a solution with standard tests ..
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    Test the series for convergence

    It must be solved by the standart test. Anyone ?
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    Test the series for convergence

    well, 1 - \sqrt[n]{n} \rightarrow 0 as n \rightarrow \infty and this will make no sense.
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    Test the series for convergence

    hello I have this one: \sum_{n=1}^{\infty} \left( 1 - \sqrt[n]{n} \right) mmmmm am sure it will be tested by using one of the comparison tests but am not getting it any help? this is not my homework, actually I finished my college 2 years ago.
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    Inverse function

    Inverse function (Edited) Homework Statement Find the inverse function of : f(x)=e^x-e^{-x}+2 where x \geq 0 Homework Equations All what I did is : y=e^x-e^{-x}+e The Attempt at a Solution How in earth can I solve this for x ?
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    Calculating where X converges

    This is the Ratio Test not the Limit Comparison Test. Also, you should write a_k not a_n.
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    To prove that these two functions meet only once

    as x becomes large, the two function tend to 1. And clearly they are increasing functions. so what do you suggest?
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    Tangent sum or difference

    40-30 \neq 15 :redface: I think you mean 45-30 :smile:
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    Multivariable Calculus Limit process

    Yes. There is a big difference in solving multivariable limits between the 2-path rule (which is y=mx .. etc) and the polar coordinates method. 2-path rule proves only that the limit D.N.E and does not prove the existence of the limit. Polar coordinates method proves both cases.
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    Multivariable Calculus Limit process

    So the limit = ? The polar coordinates works also :)
  14. S

    Natural Log and Exponential

    Clearly, k=0 is a solution. to find the another solution you need to use an advanced topic:
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    Multivariable Calculus Limit process

    Did you notice that the numerator is a difference of squares ?
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    Limes without d'hospital

    Recall the formula [which is just the M.S. for tan(x)]: tan(x)=x+\frac{1}{3}x^3+\frac{2}{15}x^5+\frac{17}{315}x^7+... Substitute this in the limit and the two "x" will be cancelled. Then devide the denominator and the numerator by x^3. and the limit will be done by the direct substitution...
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    Derivative of cos(x)^(x+7)

    y=cos^{x+7}(x) Start by taking the natural logarithmic of both sides.
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    Differential Equation Method Question

    \frac{dy}{dx}=\frac{y-x}{y+x}=\frac{y}{y+x}-\frac{x}{y+x} Use the substitution v=x+y.
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    Quick Question on Limit Comparison Test

    The comparison tests can be applied only on the postive series.
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    Linear equation

    It should be "-" not "+". Why did you change this sign?
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    Help with sum of infinite series using the root test.

    \lim_{n\to\infty} \left( \frac{n}{n+1} \right)^n = \lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^{-n} = ? Recall: \lim_{n\to\infty} \left( 1 + \frac{a}{n^k} \right)^{bn^k} = e^{ab}
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    Double integrals

    Hello, I think polar coordinates is a good choice for this one. :)
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    Can Anyone Prove why e^x= (1+x/n)^n as n approaches Infinity

    Hello, Start by using the substitution: m=\frac{n}{x} What did you get?