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Today, the editor brings you the high-level mathematics (5): the differential median theorem .
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Today's edition brings you the Mean Value Theorem of Differential.
median value theorem
1, Roll's theorem
(1) f(x) is continuous on the closed interval [a,b];
(2) f(x) can be derived within the open interval (a,b);
(3) f(x) has the same function value at the endpoint of the interval, that is, f(a)=f(b),
then there is at least a little ξ (aξb) in (a,b), so that the derivative of the function f(x) at that point is equal to zero, that is, f'(ξ)=0.
(can be used to prove uniqueness)
1, Rolle's theorem
(1) f (x) is continuous on the closed interval [a, b];
(2) F (x) is derivable in the open interval (a, b);
(3) The function values of f (x) at the end of the interval are equal, that is, f (a)=f (b), so there is at least one point in (a, b) ξ (a ξ b) , so that the derivative of function f (x) at this point is equal to zero, that is, f '(ξ)= 0 (can be used to prove uniqueness)
2. Lagrangian median theorem
3. Cauchy median theorem ( parameter equation )
Lobida rule
Applicable objects: 0 to 0 type, infinite infinity
When encountering infinite*0 type, convert one of the multipliers into the denominator and then derivate.
Applicable objects: 0 to 0 type, infinite to infinite type When encountering infinite * 0 type, convert one of the multipliers to the denominator, and then take the derivative.
Taylor formula
(low frequency when doing questions)
(Less frequently used in questions)
END
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