所屬科目:研究所、轉學考(插大)-微積分
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.