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...v2=( -3,8,-4,6)where (a,b,c,d) is as a column vector.For convenience, let u1=v1 and u2=v2+3*v1=(0,-4,2,15)we know span{v1,v2}=span {u1,u2}take u3=(0,0,1...

1ft=0.3048m，1lb=0.45359kg 假設水桶拉起高度為y，再拉起高度dy所做的功為dw 則由W=FS公式及y = v*t => t = y/v = y/2 (每秒2ft) dw=F*dy => dw=(100-0.5t)g*dy => dw=(100-0.5*y/2)g*dy (g為重力常數) W=∫(0積到100)(100-0.5*y/2)g*dy =g∫(0積到100)(100-y/4) dy (g提到外面去) =g*(100y-y^2/8 |( 0積到...

...3]  [0]                [0]  [1]∴[1]  [5]  [-1] is not in span of V

In spherical coordinates, Let x = psinθcosσ y = psinθsinσ z = pcosθ So, the equation becomes...

Let An={Xn,Xn+1,....}. (a) For a given ε>0, there exist N1 s.t. a-ε... = sup{X_n, X_(n+1), X_(n+2)............}limsup Xn = lim Rn我這邊是假設 Let An={Xn,Xn+1,....}.則 Rn = sup An直接去處理集合An會比較好證明.... 2006...

... to show that ∫Ag(x)dx=0 f is bounded function let M=sup{|f(x)| :x∈D}=sup{|g(x)|:x∈A}=M ...

... (3x-2y+4z-1)+k(2x-2y+z-3)=0 for any k. 2. Let plane E: (3x-2y+4z-1)+k(2x-2y+z-3)=0 parallel ...d(A, E)= | -3+2 -4 +5| /√(1+4+4)= 0. In general, if E contains L2 and ...

...order(a^10)=3, order(a^8)=10 Question 2 The elements in U(Z_20) are 1,3,5,7,9,11,13,17,19 By Euler...