| ucf12-002 Cubics
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| utf06-003 Find an appropriate $ f( x)$ for each of the following. \begin{alignat*}{6} a) &\lim_{x \to 2}{ f( x)} &&= 0, & f( 2) &=\frac{0}{ 0} & b) &\lim_{x \to -1}{ f( x)}&&= 2, & f( {-1}) &=\frac{0}{ 0} \\ c) &\lim_{x \to \pi}{ f( x)} &&= \infty, & f( {\pi}) &= \infty \cdot 0 & d) &\lim_{x \to 1}{ f( x)} &&= 1, & f( {1}) &=\frac{0}{ 0} \\ e) &\lim_{x \to \pi}{ f( x)} &&= 0, & f( {\pi}) &= \infty \cdot 0 & f) &\lim_{x \to d}{ f( x)} &&= 3, & f( {d}) &=\infty \cdot 0 \end{alignat*} Do you notice anything strange about the limit of $ f( x)$ as $x \to c$ when $ f( c)$ has the form $\infty \cdot 0$? |
| utf19-003 Prove the following for a rational function $r(x)=\frac{p(x) }{ q(x)}$ where $p(x)$ and $q(x)$ are polynomials.
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| utf29-001 {Newton's Law of Cooling} states that the rate of change of the temperature T of an object is proportional to the difference between T and the temperature $\tau$ of the surrounding medium: $$\frac{d T}{dt} = k (T-\tau)$$ where k is a constant.
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