4.4 Formula Sheet (Final)

4.4 Formula Sheet (Final) - Formula sheet for Final Exam in...

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Formula sheet for Final Exam in Math 106 on Monday 14, 2007 Derviative formulas ( x p ) ± = px p - 1 ( e x ) ± = e x (ln x ) ± = 1 x General properties of derivatives ( cf ) ± = cf ± ( f + g ) ± = f ± + g ± ( fg ) ± = f ± g + ± (1 /g ) ± = - g ± g 2 ( f/g ) ± = f ± g - ± g 2 ( f ( g )) ± = f ± ( g ) g ± Equation to the tangent line to the graph at x 0 : y = f ( x 0 )+ f ± ( x 0 )( x - x 0 ) Exponentials. lim n →∞ ( 1+ 1 n ) n = e =2 . 71828. Properties: x p x q = x p + q e x e y = e x + y 1 /x p = x - p 1 /e x = e - x ( x p ) q = x pq ( e x ) y = e xy h ( t )= Ae rt satisfes h ± ( t rh ( t ), h (0) = A .I F r> 0, t = (ln(2)) /r is the doubling time . IF r< 0, t = (ln(1 / 2)) /r is the half-life . Natural Logarithm. By defnition e ln x = x . This implies ln( e x x . Properties: ln( uv ) = ln( u )+ln( v ) ln(1 /u - ln( u ) ln( u/v )=ln( u ) - ln( v ) ln( u p p ln( u ) Maxima and minima, increasing, decreasing, convex, concave f is increasing where f ± ( x ) > 0, decreasing where f ± ( x ) < 0. IF f ± ( c ) = 0 then c is a critical point. (This differs From the book, but is the commonly accepted defnition). This is a necessary condition For the point c to be a local maximum [minimum], i.e., there are a<c<b so that f ( c
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4.4 Formula Sheet (Final) - Formula sheet for Final Exam in...

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