Question

Find \(lt_{x\rightarrow -33}\frac{ln(x^3+68x^2+1222x+2179)-ln(x+1)}{(x^2+66x+1089)}\)

(a) -33

(b) ^1⁄2

(c) 0

(d) ^31⁄32

I had been asked this question in semester exam.

Origin of the question is Indeterminate Forms topic in division Differential Calculus of Engineering Mathematics

Answer 1

The correct choice is (d) ^31⁄32

Easy explanation: \(=lt_{x\rightarrow -33}\frac{ln(1+\frac{(x+33)^2(x+2)}{(x+1)})}{(x+33)^2}\)

\(=lt_{x\rightarrow -33}(\frac{1}{(x+33)^2})\times(\frac{(x+33)^2(x+2)}{(x+1)}-\frac{(x+33)^4(x+2)^2}{2(x+1)^2}….\infty)\)

\(=lt_{x\rightarrow -33}(\frac{(x+2)}{(x+1)}-\frac{(x+33)^2(x+2)^2}{2(x+1)^2}….\infty)\)

\(=lt_{x\rightarrow -33}(\frac{(x+2)}{(x+1)})=\frac{(-33+2)}{(-33+1)}\)