(a) State and prove mean value theorem. (b) Evaluate : $\lim_{x \to 0…

Question

(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 series in powers of $x$ and $y$ upto third degree terms.

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