108年 - 108東吳大學_碩士班招生考試_數學系B組︰基礎數學#101160

(i)f(x)=(3x²-lnx+1)⁵

(ii)

(i)

(ii)

2. 20%
(a) 5% State the Extreme Value (Max-Min) Theorem.

(b) 15% Find the extreme values of f ( x) =− x³ + 12 x + 5 on − 3 ≤ x ≤ 3 .

3. 20%
(a) 10% Find the Taylor’s formula with remainder of order n generated by .

(b) 10% Show that the Taylor series generated by converges to f(x) for every real value of x.

1. 20%
(a) 10% Let E be an n × n elementary matrix, what is the determinant det(E) of E ?

(b) 10% Determine whether the set W of all 2 × 2 real symmetric matrices is a vector subspace of (all 2 × 2 real matrices ). Is W a finite-dimensional vector subspace?

2. 20% Find the least squares straight line fit to the four points (0,1), (1,3), (2,4) and (3,4).

108年 - 108東吳大學_碩士班招生考試_數學系B組︰基礎數學#101160

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