Formulas2

# Formulas2 - d d n f x h f x nx n-1 u = f x v = g x x = uv...

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Unformatted text preview: d d n f ( x + h) - f ( x ) nx n-1 u = f ( x ) , v = g ( x ) x = [ uv ] = u ' v + uv ' hf 0 dx h dx d x d u ' v - uv ' u dy dy du d n nu n-1 u ' = u = ex = . e = 2 dx v v dx dx du dx dx f ' ( x ) = lim d u' [ ln u ] = dx u g ' ( y0 ) = E= d u eu u ' e = dx d x a x ln a a = dx d u a u a ' a = ln u dx d 1 [ ln x ] = dx x f ( x ) - f ( a ) = f '( a ) ( x - a ) f has point f ( x ) f f ( a ) + f '( a ) ( x - a ) and g has the point 1 g ( x ) = f -1 ( x ) f ' ( x0 ) n x dx = ( x0 , y0 ) ( y0 , x0 ) x f '( x) f ( x) 1 n+1 x +C n +1 kf ( x) dx = k f ( x) dx 1 dx = ln| x | + C x a x dx = 1 x a +C ln a [ f ( x) g ( x)]dx = f ( x) dx g ( x) dx x x e dx = e + C 1 ax ax e dx = e + C a b lim n lim n lim n * f ( x k ) x = f ( x k -1 )x = f ( x k )x = f ( x) dx n k =1 n k =1 n k =1 a b a f ( x) dx = b F ( x ) = F ( b) - F ( a ) a b b a a f ( x) dx = - f ( x) dx a b b a a a f ( x) dx = 0 af f ( x) dx = a ( x) dx a b f f f ( x) dx = ( x) dx + ( x) dx a c b b b c b dx f g af ( x) + bg ( x ) = a ( x) dx + b ( x) dx a a a a b d b( t ) f ( x) dx = - F ' ( t ) = - f ( t ) f ( x ) dx = f ( b ( t ) ) b ' ( t ) - f ( a ( t ) ) a ' ( t ) t dt a( t ) 1 n+1 1 u u n dx = ln| u | + C e du = e + C u du = u +C u n +1 u dv = uv - v du f ( x) dx = F ' ( t ) = f ( t ) d dt d dt t FA07 T2A 2007 Arizona State University, Department of Mathematics and Statistics 1 ...
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