ASSIGNMENT – 2 FOR ENGINEERING MATHEMATICS – I

\[\LARGE {\color {red}{Questions\ from\ Unit-III\ and\ Unit-IV}}\]
\[1.\ Show\ that\ \frac{1\ -\ Cos\ 2A\ +\ Sin\ 2A}{1\ +\ Cos\ 2A+\ Sin\ 2A}\ =\ Tan\ A\ \hspace{15cm}\]
\[2.\ Prove\ that\ Cos\ 10^{0}\ Cos\ 50^{0}\ Cos\ 70^{0}\ =\ \frac{\sqrt{3}}{8}\ \hspace{15cm}\]
\[3.\ Evaluate:\ \lim\ _{x\ \to\ 2}\ \frac{x^3\ -\ 8}{x^4\ -\ 16}\ \hspace{15cm}\]
\[4.\ Find\ \frac{dy}{dx}\ (i)\ if\ y\ =\ (x^2\ +\ 3)\ Cos\ x\ Log\ x\ \hspace{2cm}\ (ii)\ y\ =\ \frac{x^2\ -\ 1}{e^x}\ \hspace{7cm}\]

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