| utf04-003 What is the ratio of the areas of the inner and outer hexagons in this figure? |
| utf04-004
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| utf04-005 Let $$ f( x) = \frac{x^2 -1 }{ x+1}$$
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| utf10-002 Assume that $ f( x)$ is a differentiable function and that the values of $ f( x)$ and its derivative at the points $x=0,1,2,$ and $3$ are given by: \begin{alignat*}{4} f( 0) &= 3 & f( 1) &= 5 & f( 2) &= -2 & f( 3) &= 6 \\ f'( 0) &= -1 & f'( 1) &=0 & f'( 2) &= 3 & f'( 3) &=1 \end{alignat*} Let $ g(x) = x^2 - 3x + 2.$ For each function below calculate the derivative at the given point. \begin{align*} a)& \frac{ f( x) }{ g(x)} & x=0 b)& f( x) g(x) ; x=1 \\ c)& f( { g(x)}) ; x=2 d) g({ f( x)}) ; x=3 \end{align*} |
| utf10-003 Differentiate the following. \begin{alignat*}{2} &a) f( x) = (1+\sqrt x)^{\frac{1}{ 2}} & &b) g(x) = [(x^2+1)^2 + (x^2 + 1) + 1 ]^2 \\ &c) f( x) = [ x - \frac{2 }{ x + \sin x}]^{{-1}} & &d) f( x) = \sin {(\frac{\cos x }{ x})} \\ &e) f( x) = (\sin^2 x)(\sin {x^2})(\sin^2 {x^2}) & &f) f( x) = \frac{\sin (\cos x) }{ x} \end{alignat*} |