IGNOU MMT 4 2026 - Obtain the second Taylor’s series expansion for the function giv

Question

Obtain the second Taylor’s series expansion for the function given by

$$f(x, y) = xy^2 + 5xe^y \text{ at } \left(1, \frac{\pi}{2}\right).$

09 Jan 2026

Answer :

Word Count : 325

दी गई फ़ंक्शन है: [ f(x, y) = xy^2 + 5x e^y ] हमें इसका दूसरा टेलर विस्तार बिंदु ((1, \pi/2)) के पास निकालना है। चरण 1: आंशिक अवकलज निकालना 1. पहले क्रम के आंशिक अवकलज: [ f_x = \frac{\partial f}{\partial x} = y^2 + 5 e^y ] [ f_y = \frac{\partial f}{\partial y} = 2xy + 5x e^y ] 2. दूसरे क्रम के आंशिक अवकलज: [ f_{xx} = \frac{\partial^2 f}{\partial x^2} = 0 ] [ f_{yy} = \frac{\partial^2 f}{\partial y^2}

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