Q&A

Post on this page, in the comments below, any questions you have on your maths study. Some I may be able to answer right here in these comments. Others, that are more involved, I will answer in a blog post.

I make no guarantees about the timeframe in which I’ll be able to answer questions. So if you’re asking a question at 3am on the night before an exam, don’t blame me if I don’t answer in time and you end up flunking. You’ve got bigger problems :)

This page is open to the public, but I will obviously prioritise questions from my own students.

6 thoughts on “Q&A”

    1. Hi Totally Not Steve.

      To solve the equation you need to get \boldsymbol{x} by itself on one side of the equation. This is my solution:

      \boldsymbol{3x+4=19}
      \boldsymbol{3x=15}
      \boldsymbol{x=5}

      Let me know if you’re not sure what I did at each step.

  1. im getting stuck on the sin(xy) of this implicit differentiation problem.

    ycos(x) = 1 +sin(xy)

    could anyone help me?

    1. Use Chain Rule. A similar term not requiring implicit differentiation would be: If \boldsymbol{y=\sin(3x^2)}, then

      \boldsymbol{\frac{\text{d}y}{\text{d}x}=\cos(3x^2)\times (3x^2)'=\cos(3x^2)\times 6x=6x\cos(3x^2)}

      The only difference with your problem, is that you have to employ implicit differentiation to find the derivative of \boldsymbol{xy}. But if you’re ok with differentiating \boldsymbol{y\cos(x)} that shouldn’t be a problem.

      Hope that helps. I’ll write a larger post in the blog on implicit differentiation when I get the opportunity.

  2. Hi, I’m confused about a problem: Use long division and partial fractions to simplify the rational function (x^4+x^3-x^2-x+1)/(x^3-x).

    I’m confused on whether I should use partial fractions or long division, I get different answers for each method. I have also tried doing partial fractions and then long division and I get the answer: x+1-(1/(x^3-x)). Is this correct?

    Thanks

    1. You use both. Using long division gives the result you already have: x+1-1/(x^3-x). I haven’t double-checked this result for calculation errors but it’s certainly of the correct form.

      Then the fraction 1/(x^3-x) can be simplified using partial fractions.

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