GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Question : 23 of 65

Marks: +1, -0

For a small value of

{h}

, the Taylor series expansion of

{f}( {x}+ {h})

$f(x)-h f^{'}(x)+\;{h^{2}}/{2} f^{' '}(x)-\;{h^{3}}/{3} f^{' ' '}(x)+. . . ∞$
$f(x)+h f^{'}(x)+\;{h^{2}}/{2 !} f^{' '}(x)+\;{h^{3}}/{3 !} f^{' ' '}(x)+. . . ∞$
$f(x)-h f^{'}(x)+\;{h^{2}}/{2 !} f^{' '}(x)-\;{h^{3}}/{3 !} f^{' ' '}(x)+. . . ∞$
$f(x)+h f^{'}(x)+\;{h^{2}}/{2} f^{' '}(x)+\;{h^{3}}/{3} f^{' ' '}(x)+. . . ∞$

Solution:

For the small value of

{h}

, the Taylor's series expansion of

f(x+h)=\;{f(x)}/{0 !}+\;{h f^{'}(x)}/{1 !}+\;{h^{2}}/{2 !} f^{' '}(x)

+\;{h^{2}}/{3 !} f^{' ' '}(x)+. . ., ∞

f(x+h)=f(x)+h f^{'}(x)+\;{h^{2} f^{' '}(x)}/{21}

+\;{h^{2}}/{31} f^{' ' '}(x)+. . . . ∞

So option (b) is correct

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