Question

Find \(lt_{x\rightarrow 1012345}(\frac{[sinh(x)]^2-[cosh(x)]^2}{[sinh(x)]^2+[cosh(x)]^2})\)

(a) ^1⁄cosh(1012345)

(b) 90987

(c) 1012345

(d) ∞

The question was posed to me in an interview.

This question is from Indeterminate Forms topic in chapter Differential Calculus of Engineering Mathematics

Answer 1

Right choice is (a) ^1⁄cosh(1012345)

Easy explanation: \(lt_{x\rightarrow 1012345}\left ( \frac{1}{(\frac{(e^x+e^{-2x})^2+(e^x-e^{-x})^2}{4})}\right )\)

\(=lt_{x\rightarrow 1012345}\frac{1}{\frac{(e^{2x}+e^{-2x})}{2}}=\frac{1}{cosh(1012345)}\)