| utf03-003 Let $S$ be the relation $ \{ (x,y) | (x^2-4)y= x^2 + 2x \}$.
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| utf03-006 Which of the graphs below could correspond to the following functions? {Match them.} \begin{alignat*}{4} &a) \text{odd power function}\hphantom{\text{log x}} & &b) \text{ even power function} & &c) \text{a quadratic}\\ &d) \log x & &e) \text{a 4th degree polynomial} & &f) b^x \\ &g) \sin x & &h) (\frac{1}{ 2})^x & &i) \text{absolute value} \end{alignat*} |
| utf04-007 Compute the following limits (think about the {theorems} you use). \begin{alignat*}{3} &a) \lim_{x\to 1} \frac{x^3-1 }{ (x-1)^2} & &b) \lim_{x\to{-2}} \frac{x^3 + 8 }{ x+2} & &c) \lim_{x \to 1} \frac{x^3-2x^2 + 2x -1 }{ x^3 -1} \\ &d) \lim_{x\to 8} \frac{\root 3 \of x - 2 }{ x-8} & &e) \lim_{x\to{-1}} \frac{\frac{1}{ x}+ 1}{x+1} & &f) \lim_{x \to a} \frac{x^n - a^n }{ x-a} \\ &g) \lim_{x\to 2} \frac{\sqrt 2 - \sqrt x }{ 2-x} & &h) \lim_{x \to 0}\frac{1- \sqrt{1-x^2} }{ x^2} & &i) \lim_{x \to 4} \frac{\root 3 \of x - \root 3 \of 4 }{ x-4} \end{alignat*} |
| utf07-002 Match each of the derivatives shown below with the corresponding functions. Which functions shown below are continuous? Which derivatives shown below are continuous? Explain what shapes continuous functions must have to produce jump discontinuities in the derivative and asymptotes in the derivative. Draw a continuous function whose derivative has a jump discontinuity at $x=1$ and an asymptote at $x=5$; draw the derivative. |
| utf07-006 The function $ s(t) = \alpha t^2 + \beta t + \gamma$ gives the position of a free-falling object at time $t$.
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