60 - Calculus Questions Answers

length for one turn = 3

Draw diagonal of a rectangle then turn it as a cylinder, you will get the construction given in the question.

$$\begin{gathered} In triangle l = \sqrt{3^2+n^2} \\ So total length of wire having n turn = n\sqrt{3^2+n^2} \\ Compare with 20 and solve \end{gathered}$$

$$\begin{gathered} The general solution of this kind of \\ differential eq. is y = e^{ax} \\ Let a function g\left(x\right) = e^{ax}f\left(x\right) \left(1\right) \\ differentiate eq. \left(1\right) thrice for getting g^{,,,}\left(x\right) \\ now for getting the same function as given \\ find a. you get the same function for \\ a = 1/2. clearly, for min 5 zeros of g\left(x\right), \\ there are min 2 zeros for g^{,,,}\left(x\right). \\ solve and inform if face any problem. \end{gathered}$$

1+x²+x⁴ = (1+x+x²)(1-x+x²)

now solve