Advanced CalculusSeths and functions; Continuity; Defferentiation; Integration; Series; Uniform convergence; Diferentiation of transformations; Aplications to geometry and analysis; Differential geometry and vector calculus; Numerical methods. |
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Page 118
... Theorem 3 ( Mean Value Theorem ) Let f be continuous on [ a , b ] , and let f ' ( x ) exist for a < x < b . Then , at least one point x , exists interior to [ a , b ] such that ( 3-2 ) f ( b ) f ( a ) = ( b− a ) ƒ ' ( x 。) Theorem 4 ...
... Theorem 3 ( Mean Value Theorem ) Let f be continuous on [ a , b ] , and let f ' ( x ) exist for a < x < b . Then , at least one point x , exists interior to [ a , b ] such that ( 3-2 ) f ( b ) f ( a ) = ( b− a ) ƒ ' ( x 。) Theorem 4 ...
Page 119
... value we found for K , we obtain ( 3-3 ) . Suppose now that g ( b ) − g ( a ) = 0. We cannot now solve for K ... theorem to g . The geometric meaning of the general mean value theorem is very similar to that of the ordinary mean value ...
... value we found for K , we obtain ( 3-3 ) . Suppose now that g ( b ) − g ( a ) = 0. We cannot now solve for K ... theorem to g . The geometric meaning of the general mean value theorem is very similar to that of the ordinary mean value ...
Page 120
... value theorem to obtain a simple approximation to a special function . Theorem 5 When u > 0 and v≥ 0 , √u2 + v may ... mean value theorem , there is an xo , 0 < x 。< v , with - ƒ ( v ) = f ( 0 ) + ( v − 0 ) ƒ ' ( x 。) v = u + 2√u2 ...
... value theorem to obtain a simple approximation to a special function . Theorem 5 When u > 0 and v≥ 0 , √u2 + v may ... mean value theorem , there is an xo , 0 < x 。< v , with - ƒ ( v ) = f ( 0 ) + ( v − 0 ) ƒ ' ( x 。) v = u + 2√u2 ...
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