Calculus Lab Activity Review
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Questions and Answers

In Lab activity 1.2.4, what function is used to find the difference quotient?

  • $f(x) = x$
  • $f(x) = x^3$
  • $f(x) = x^4$
  • $f(x) = x^2$ (correct)
  • Which limit expression is used in Lab activity 2.3.4?

  • $\lim_{h \to 0} \frac{f(a+h) - f(a)}{h^2}$
  • $\lim_{h \to \infty} \frac{f(a+h) - f(a)}{h}$
  • $\lim_{a \to 0} \frac{f(a+h) - f(a)}{h}$
  • $\lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$ (correct)
  • During the differentiation proof in Lab activity 2.3.4, which algebraic identity is used for rationalizing the denominator?

  • $a^2 + b^2 = (a+b)^2$
  • $a^2 - 2ab + b^2 = (a-b)^2$
  • $a^2 + 2ab + b^2 = (a+b)^2$
  • $a^2 - b^2 = (a-b)(a+b)$ (correct)
  • In Lab activity 2.3.4, given $f(x) = \sqrt{x}$, which expression represents $f(a+h)$?

    <p>$\sqrt{a+h}$</p> Signup and view all the answers

    In the differentiation process shown, what final expression is obtained for $\frac{d}{dx} \sqrt{x}$?

    <p>$\frac{1}{2\sqrt{a}}$</p> Signup and view all the answers

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