Let D2 be the operation of taking the second derivative. Find the image of 2x^2+3x^2-5x+4 under D2. Prove that D2 is a linear operator on Pn. Determing the kernel and range of D2.
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D is linear operator,since
D(f+g)=D(f)+D(g) and D(kf)=kD(f) for any .
D(f)=0 if and only if .
D(Pn)= if n is greater than 2.
Last edited by Shanks; December 6th 2009 at 07:15 PM.
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