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SMA_01
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Homework Statement
Use Taylor's Theorem to show that
√(x+1)=1+(1/2)x+O(x2)
for x sufficiently small.
Here's what I did:
f(x)= √x+1
f'(x)= (1/2)(x+1)(-1/2)
Then using x0=0,
f(0)= 1, f'(0)=1/2.
√x+1=1+(1/2)x-(1/8)x2(cx+1)(-3/2)
So, then using h as a parameter:
l√(h+1) -1-(1/2)h l ≤ 1/8(h2)
Finally,
√(h+1) = 1+(1/2)h+O(h2)
Is this correct?
I' m having difficulty understanding the meaning of O, can someone please explain in simple terms?
Thank you.
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