f(x) = tan^-1(x) (A) What's the remainder E1(x) in Taylorrs formula f(x) = P1(x) + E1(x)? (B) Use Taylors formula with remainder to estimate tan^-1(x) = (pi)*1/4. (C) Show that the remainder E1(1) lies between -1 and 0 and that (pi)*1/4 equals P1(1) - 1/4 = 3/4 with error less than 1/4.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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f(x) = tan^-1(x)

(A) What's the remainder E1(x) in Taylorrs formula f(x) = P1(x) + E1(x)?

(B) Use Taylors formula with remainder to estimate tan^-1(x) = (pi)*1/4.

(C) Show that the remainder E1(1) lies between -1 and 0 and that (pi)*1/4 equals P1(1) - 1/4 = 3/4 with error less than 1/4. 

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