103年 - 103 國立嘉義大學_碩士班(乙組)招生考試試題_應用數學系：基礎數學#146058

科目：研究所、轉學考(插大)-基礎數學 | 年份：103年 | 選擇題數：0 | 申論題數：14

試卷資訊

所屬科目：研究所、轉學考(插大)-基礎數學

選擇題 (0)

申論題 (14)

1. Evaluate the limit: (5%)
2. Find an equation for the tangent line to the curve y=F(x) at the point P wherex=1 and(5%)
3. Calculate =? where [x] it the greatest integer n such that .(5%)
4. Find the points on the graph of that are closest to the point P(0, 2).(5%)
5. Show that the integral diverges if .(10%)
6. Given the function . Find
(a) relative extrema ；
(b)point(s) of inflection ；
(c)sketch the graph.(10%)
7. The region between the curve , , and the x-axis is revolved about the x-axis togenerate a solid. Find its volume.(10%)
二、線性代數部分：
1. Find the matrix A whose eigenvalues are 4 and 1 and whose eigenvectors areand , respectively.(10%)
2. Given the matrix
(1) Find an invertible matrix P such that is a triangular matrix.(8 %)
(2) Compute = ?(7 %)
3. Let T:→ be a linear transformation. Prove that T is one to one if and only ifT is onto.(10%)
4. Find the column space of the matrix , the dimension of thecolumn space and the determinant of A, det(A).(15%)