Taylor Series
Curriculum and historical examination lineage for Taylor Series under Unit 2 (Functions of Several Variables) of Calculus And Linear Algebra (21MAB101T) at SRMIST.
Historical appearance distribution across SRMIST Formative Tests (CT1, CT2) and University End Semester examinations.
Factual marks weightage of questions asked on this topic in historical examinations.
Question templates that recur across multiple examination cycles with similar conceptual stems.
“Find the Taylor series expansion of e^{xy} at (1, 1) upto third degree terms.”
“Using Taylor's Series expand e^x \log(1 + y) up to third degree term in the neighborhood of Origin.”
“Expand $f(x,y) = e^x \sin y$ in powers of $(x-1)$ and $(y - \pi/2)$ up to the second degree terms...”
“Expand $f(x,y) = xy + 3y - 2$ in powers of $(x-1)$ and $(y+2)$ up to second degree terms using...”
“Answer part a or b (a) Are the functions u = \frac{x + y}{1 - xy} and v = \tan^{-1} x + \tan^{-1} y...”
Representative historical questions extracted directly from SRMIST examination papers.
Using Taylor's Series expand e^x \log(1 + y) up to third degree term in the neighborhood of Origin.
Expand $f(x,y) = e^x \sin y$ in powers of $(x-1)$ and $(y - \pi/2)$ up to the second degree terms using Taylor's theorem.
Expand $f(x,y) = xy + 3y - 2$ in powers of $(x-1)$ and $(y+2)$ up to second degree terms using Taylor's theorem.
Answer part a or b (a) Are the functions u = \frac{x + y}{1 - xy} and v = \tan^{-1} x + \tan^{-1} y functionally dependent? If so, find the relation between them. --- OR --- 22....
Find the Taylor series expansion of e^{xy} at (1, 1) upto third degree terms.
Examinations where questions for Taylor Series have appeared.
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