Home › Previous year questions › GATE 2019 CE (CE1) › Question 14GATE 2019 CE (CE1) – Question 14 Engineering Mathematics · Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series · 1 mark · Multiple choice
For small h, which is the Taylor expansion of f(x+h)?
$f(x)+hf^\prime(x)+\frac{h^2}{2!}f^{\prime\prime}(x)+\frac{h^3}{3!}f^{\prime\prime\prime}(x)+\cdots$ $f(x)-hf^\prime(x)+\frac{h^2}{2!}f^{\prime\prime}(x)-\frac{h^3}{3!}f^{\prime\prime\prime}(x)+\cdots$ $f(x)+hf^\prime(x)+\frac{h^2}{2}f^{\prime\prime}(x)+\frac{h^3}{3}f^{\prime\prime\prime}(x)+\cdots$ $f(x)-hf^\prime(x)+\frac{h^2}{2}f^{\prime\prime}(x)-\frac{h^3}{3}f^{\prime\prime\prime}(x)+\cdots$ Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (A) $f(x)+hf^\prime(x)+\frac{h^2}{2!}f^{\prime\prime}(x)+\frac{h^3}{3!}f^{\prime\prime\prime}(x)+\cdots$
Explanation Taylor’s theorem gives $$f(x+h)=f(x)+hf^\prime(x)+\frac{h^2}{2!}f^{\prime\prime}(x)+\frac{h^3}{3!}f^{\prime\prime\prime}(x)+\cdots.$$ Answer **A**. B reverses the odd-power signs; C and D use 3 instead of 3! in the cubic term.