(a) Determine $\lim_{x \to 0} \left(\frac{\tan x}{x}\right)^{1/x^2}$.…

Question

(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 degree terms.

(c) State and prove mean value theorem.

Related pages

• Taylor's Series in Two Variables — topic
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