Seminar -1 for Enginnering Mathematics – I

\[Group\ 1:\ Solve\ by\ using\ Cramers\ Rule\ \hspace{20cm}\]

\[3x – y + 2z=8,\ x – y + z = 2\ and\ 2x + y – z = 1\ \hspace{15cm}\]

\[Group\ 2:\ If\ Tan\ A\ =\ \frac{1}{2} \ and\ Tan\ B\ =\ \frac{1}{3},\ find\ the\ value\ of\ Tan(A\ +\ B)\ \hspace{15cm}\]

\[Group\ 3:\ If\ Cos\ θ\ =\ \frac{1}{3},\ find\ Cos\ 3θ\ \hspace{15cm}\]

\[Group\ 4:\ Prove\ that\ \frac{Sin\ 3θ}{Sin\ θ}\ -\ \frac{Cos\ 3θ}{Cos\ θ}\ =\ 2\ \hspace{15cm}\]

\[Group\ 5:\ If\ a\ =\ Sin\ x\ +\ Sin\ y,\ b\ =\ Cos\ x\ +\ Cos\ y,\ Prove\ that\ a^2\ +\ b^2\ =\ 4\ Cos^2\ (\frac{x\ -\ y}{2})\ \hspace{15cm}\]

\[Group\ 6:\ Show\ that\ Tan^{-1}\ (\frac{x\ -\ y}{1\ +\ x\ y})\ =\ Tan^{-1}\ x\ – Tan^{-1}\ y\ \hspace{15cm}\]

\[Group\ 7:\ Evaluate:\ \lim\ _{x\ \to\ 3}\ \frac{x^5\ -\ 3^5}{x^4\ -\ 3^4}\ \hspace{15cm}\]

\[Group\ 8:\ Find\ \frac{dy}{dx}\ if\ y\ =\ \frac{e^x\ +\ Sin\ x}{1\ -\ Cos\ x}\ \hspace{15cm}\]