Taylor's Series in Two Variables — Study Resources & PYQs
Taylor's series expansion for functions of two variables.
- Estimated study time: 70 minutes
Study resources
- GeeksforGeeks – Taylor Series (Theorem, Proof, Formula) (Article) — Taylor's theorem, expansion formula and applications, with the link to the Maclaurin form (centre x = 0).
- NIST DLMF – Calculus of Two or More Variables (Article) — Authoritative reference for Taylor's theorem in two variables, maxima/minima tests and multiple integrals. Use for the precise two-variable formula.
- MIT OpenCourseWare — Multivariable Calculus (Article) — MIT multivariable-calculus materials covering partial derivatives, homogeneous-function ideas, Taylor expansions, extrema and Lagrange multipliers.
- MIT OpenCourseWare — Linear Algebra (Article) — MIT linear-algebra materials covering matrices, rank, elementary operations, eigenvalues/eigenvectors, Cayley-Hamilton-related concepts and diagonalization.
Taylor's Series in Two Variables previous year questions
- (a) Using Taylor series expansion, express $f(x,y) = xy^2 + 3x - 2$ in powers of $x + 2$ and $y - 1$. (b) Find the extreme values of the function $f(x,y) = x^3…
- (a) Using Taylor series expansion, express $f(x,y) = xy^2 + 3x - 2$ in powers of $x + 2$ and $y - 1$. (b) Find the extreme values of the function $f(x,y) = x^3…
- (a) State and prove mean value theorem. (b) Evaluate : $\lim_{x \to 0} \left(\frac{1}{x^2} - \frac{1}{x \sin x}\right)$. (c) Expand $f(x, y) = e^{x+y}$ as a se…
- (a) Determine $\lim_{x \to 0} \left(\frac{\tan x}{x}\right)^{1/x^2}$. (b) Expand $f(x, y) = e^x \log(1 + y)$ as a series in powers of $x$ and $y$ upto third de…
Taught in these subjects
- ENGINEERING MATHEMATICS-I — BMAT11 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BMAT11 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BST1101 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BST1101 · Government College of Engineering and Technology, Jammu