Calculus Quiz on Derivatives and Integrals
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Questions and Answers

What is the $n^{th}$ derivative of $y = rac{d^n}{dx^n}( ext{sin }x)$?

  • $(-1)^{n} ext{sin }(x + n rac{ ext{ extpi}}{2})$ (correct)
  • $(-1)^{n} ext{cos }(x + n rac{ ext{ extpi}}{2})$
  • $ ext{sin } x$
  • $ ext{cos } x$
  • What does $ rac{d^{2} z}{d x^{2}}$ equal when $z = au + bv$ and $y = au - bv$?

  • $ rac{d^{2} u}{d x^{2}} + rac{d^{2} v}{d x^{2}}$
  • $0$
  • $2a rac{d^{2} u}{d x^{2}} + 2b rac{d^{2} v}{d x^{2}}$ (correct)
  • $ rac{d^{2} y}{d x^{2}}$
  • What is the result of evaluating $ rac{d^{2} z_{i}}{d x_{i}^{2}}$ where $z_{i} = x_{i}^{2}$?

  • $0$
  • $4 x_{i}$
  • $x_{i}$
  • $2$ (correct)
  • What is the integral $ rac{ ext{∫}_{0}^{ rac{ ext{ extpi}}{2}} ext{sin}^2(x) dx}$ equal to?

    <p>$ rac{ ext{ extpi}}{4}$</p> Signup and view all the answers

    What will be the value of $m$ if $ rac{ ext{∂} V}{ ext{∂} x} (2, -3, 4) = m$ for $V = (x^{2} + y^{2} + z^{2})$?

    <p>$15$</p> Signup and view all the answers

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