| utf10-004
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| utf10-009 Find $ f'( x)$ in terms of $ g(x)$ and $ {g'}(x)$, where $ g(x) > 0$ for all x. {(Recall: If c is a constant, then $ g(c) $ is a constant.)} \begin{alignat*}{3} &a) f( x) = g(x) (x-a) & &b) f( x) = g(a) (x-a) & &c) f( x) = g({x+g(x)}) \\ &d) f( x) = \frac{ g(x) }{ x-a} & &e) f( x) = \frac{1 }{ g(x)} & &f) f( x) = g({x g(a)}) \\ &g) f( x) = \sqrt {{ g(x)}^2} & &h) f( x) = \sqrt { g({x^2})} & &i) f( {2x+3}) = g({x^2})\\ &&&&&\text{{Hint:}} x = 2\frac{(x-3) }{ 2} + 3 \\ \end{alignat*} |
| utf10-010 Find $ f'( 0)$ if $$ f( x) = \begin{cases} g(x) \sin (\frac{1}{ x}), & x \neq 0 \\ 0, & x = 0, \end{cases}$$ and $$ g(0) = {g'}(0) = 0.$$ |
| utf13-002 A spherical balloon is inflated with gas at the rate of 100 cubic feet per minute. Assuming that the gas pressure remains constant, how fast is the radius of the balloon increasing at the instant when the radius is $a)3ft. b)10ft. c)100ft.$ |
| utf13-005 Two airplanes are flying north at the same height on parallel paths ten miles apart with speeds of $400$ and $600$ miles per hour. How fast is the distance between the planes changing when the slow plane is five miles further north than the fast one? |