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IOE 2079 Baishakh Engineering Mathematics-1 Old is Gold Solution | Part-1 | Er. Brijkishor Jaiswal

IOE 2079 Baishakh Engineering Mathematics-1 Old is Gold Solution | Part-1 | Er. Brijkishor Jaiswal

Pdf solution: https://drive.google.com/file/d/1rV5Q-J4ddVfknXwhRQ-t7eLNDpuierw3/view?usp=sharing
IOE Old is Gold Question Collection: https://drive.google.com/file/d/1-z-1mHCy6jVw6ZBvdsrAV0I-Cbfs-QWz/view?usp=sharing

Questions Discussed:

01:52 1. State Leibnitz’s theorem. If \( y = \log(x + \sqrt{a^2 + x^2}) \) then using the theorem show that
\((a^2 + x^2)y_2 + xy_1 = 0\) and hence show that
\((a^2 + x^2)y_{n+2} + (2n+1)xy_{n+1} + n^2 y_n = 0\).
**[1+4]**

14:26 2. Assuming the validity of expansion, find the expansion of: \(\log(\sec x)\) by using Maclaurin’s theorem.
**[5]**

23:00 3. What do you mean by indeterminate form? State various forms of indeterminacy. Evaluate
\[
\lim_{x \to 0} \left(\frac{\sin x}{x}\right)^x
\]
**[5]**

33:11 4. Define asymptotes and its types. Find the asymptotes of the curve
\[
x^3 + 4x^2y + 5xy^2 + 2y^3 + 2x + 4xy + 2y^2 - x - 9y + 1 = 0.
\]
**[1+4]**

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