107年 - 107 東吳大學_碩士班招生考試_數學系(B組)：基礎數學#101987

科目：研究所、轉學考(插大)-基礎數學 | 年份：107年 | 選擇題數：0 | 申論題數：5

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所屬科目：研究所、轉學考(插大)-基礎數學

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申論題 (5)

1. Find the tangent line of the curve 
sin(x+ y) +cos(r-y)=y at the point (x, y)=615d17da05a1d.jpg
2. Find the Taylor formula of the function 
f(x) = cos(x2) with respect to x = 0 up to the 8-th degree, and prove that I 615d180caa555.jpg
3. Graph the curves of functions y = x3 + 2x2 and y = 3x on the same ry-coordinate. Find the area bounded by the two curves.
4. Consider the matrix 
615d1996e2200.jpg
 Find a basis for the column space, the row space and the null space of A respectively.

5. Diagonalize the matrix 615d19afe1d68.jpg. Compute 615d19c350fab.jpg, k is a natural number.