Recent content by appplejack

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    Indefinite integral involving arctan and ln

    Homework Statement ∫ 1/x arctan (lnx) dx Homework Equations The Attempt at a Solution 1.U substitution. SO u = ln x, du= 1/x dx ∫ arctan u du 2.by parts: u = arctan u du = 1/ 1+u^2 v = 1 dv = du 3. uv - ∫vdu = artan u - ∫ 1/ 1+u^2 =...
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    Integration involving partial fraction

    Yes. I just need to check the answer.
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    Integration involving partial fraction

    Homework Statement I want to check the answer to this question. ⌠ 2 x dx / (x+1) (x+2) ⌡ 1 Homework Equations The Attempt at a Solution For partial fraction I got A= -1 and B = 2 My final answer is -ln 2 + ln4 - ln3 = ln 4/ ln2 * ln 3
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    Proving the Inverse Relationship of ln(x) and e^x

    Homework Statement How do you prove ln(e^x) = x? Homework Equations The Attempt at a Solution I just memorized this but want to know how I can prove this
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    Limit of sin4x/3x as x approaches 0: Squeeze Theorem

    Yeah you're right.So, It's true that limit u->0 of sin(u)/u=1?
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    Limit of sin4x/3x as x approaches 0: Squeeze Theorem

    Homework Statement Find lim sin4x/3x x -> 0 Homework Equations The Attempt at a Solution I did some algebraic massaging and got sin4/3x = 4/4 * sin4x/3x = 4/3 * sin4x/4x but I don't understand how sin4x/4x becomes 1 like my textbook says so.
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    Solving Epsilon-Delta Proof: Homework Statement

    Homework Statement I just want to make sure I include all the steps in doing this: lim (6x-7) = 11 x->3 Homework Equations The Attempt at a Solution given ε>0, we need to find a δ>0, such that 0< lx-3l < δ then 0 < l (6x-7)-11 l < ε To prove this I need to make 0 < l...
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    Does (1+1/n)^2n converge or diverge? And how to approach arctan x?

    Homework Statement I need to find whether the sequence converges or diverges 1.(1+ 1/n)^2n 2.arctan x Homework Equations The Attempt at a Solution 1. My answer is wrong but I don't know how I can get the right answer My answer (1 + 1/n) ^2n becomes 1 because 1/n tends to...
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    Increasing and descreasing function question

    I'm weak on trig. For 1 + sinx, does it shift the graph upward by 1 because y intercept is 1 when x=0? And the graph of sine goes up and down. That's why I doubt that the function increases all the time. I know that I'm wrong but I'm still wondering why.
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    Increasing and descreasing function question

    Thanks for your help but I think I need to work on trig. Could you explain why 1 + sinx is always ≥ 0?
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    Increasing and descreasing function question

    Homework Statement I've got two questions 1.Find the intervals on which f increases and and the intervals on which f decreases. f(x)= x-cosx, 0≤x≤2∏ 2. Why is f(x) = -2sin2x - 2sinx = -2sinx (2cosx + 1) How can you factor 2cosx from the function on the left side? Homework Equations...
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    Integration Problem involving absolute bracket, sine,cosine

    Homework Statement Evaluate ∫(1)to(-1) l sin(x) l dx Homework Equations The Attempt at a Solution If I just leave it like this, is it wrong? 1. ∫(1)to(-1) l sin(x) l dx = l -cos (x)l 2. l -cos (1) l — l -cos (-1)l = 0 - 0 = 0
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    Why is the fundamental theorem of calculus astounding?

    Homework Statement I just learned this idea from my lecture in calculus. I think I understand it at a surface level but don't know much about why it is an astounding discovery as my lecturer suggested. Homework Equations So, it states that let (f) be a continuous on an interval [a,b]. Let...
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    Taking the derivative of a function (looks easy but I don't know how to do it)

    haha. Why didn't I see that? Thanks guys.
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    Taking the derivative of a function (looks easy but I don't know how to do it)

    Homework Statement f(x) = x(x-5)^4 Homework Equations The Attempt at a Solution I used product rule and chain rule so, 1(x-5)^4 + 4x(x-5)^3(1) The answer to this question is 5(x-5)^3(x-1). I left it like the answer above. I don't know how to expand (x-5)^4. Thanks.