112年 - 112 國立陽明交通大學_碩士班入學招生試題_統計學研究所﹕微積分與線性代數#130252

1.  Use the Taylor polynomial of degree 2 at x = 0 to approximate √63. (the answer should be a fraction with simplest from)

(i)

(ii)

(iii) if and only if Q=P

3.  The "norm" of a real n×n matrix A is defined as

where denotes the Euclidean norm of x. If , find .

4.  Find a basis for the intersection of the subspaces V₁ = Span((1,0,1,1), (1,1,0,1)) and V₂ = Span((0,1,1,0),(2,-1,0,2)) ⊂ . 

5.  Find the value of a such that curves y = and y = are tangent at some points also find the tangent line at that points.