2 votes 2 votes Find the value of above limit. How to approach with this type of infinity power infinity problems ?? im thinking like first we should convert this to 1 power infinity problem and then solve?? is it correct ?? please solve above que Mathematical Logic calculus limits engineering-mathematics + – Anjan asked Jan 25, 2018 Anjan 599 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Shubhanshu commented Jan 25, 2018 reply Follow Share Is it $1?$ 0 votes 0 votes Anjan commented Jan 25, 2018 reply Follow Share yes , please explain ......... 0 votes 0 votes Shubhanshu commented Jan 25, 2018 i edited by Shubhanshu Jan 25, 2018 reply Follow Share Simply take $t = \frac{1}{n}$ Now when $n \rightarrow \infty \text{ (approaches to)}$ then $t \rightarrow 0 \text{ (approaches to)}$ And put in the above expression. Then plugin t = 0. You get $({\frac{2}{3}})^0$ which is 1. 1 votes 1 votes Anjan commented Jan 25, 2018 reply Follow Share Now when n→0 (approaches to)n→0 (approaches to) then t→0 (approaches to) this is wrong i think when n->0 then t-> to infinity........?? 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes $\large \lim_{n\rightarrow \infty} \left ( \frac{2n^{2}}{3n^{2}+1} \right )^{\LARGE \frac{-3n+{2}}{5n^{2}-3}}$ Let n = $\large \frac{1}{t} $ $\large \lim_{t\rightarrow 0} \left ( \frac{\frac {2}{t^{2}}}{\frac {3}{t^{2}}+1} \right )^{\LARGE \frac{\frac {-3}{t} +{2}}{\frac {5}{t^{2}}-3}}$ $\large \lim_{t\rightarrow 0} \left ( \frac{2}{3 + t^{2}} \right )^{\LARGE \frac{t(-3 +{2t})}{5-3t^{2}}}$ $\large \left ( \frac{2}{3 + 0^{2}} \right )^0$ The answer is $ 1$ Mk Utkarsh answered Mar 14, 2018 Mk Utkarsh comment Share Follow See all 3 Comments See all 3 3 Comments reply Mk Utkarsh commented Mar 18, 2018 reply Follow Share yeah i'm not good with calculus. can you post the correct answer? 0 votes 0 votes ankitgupta.1729 commented Mar 18, 2018 reply Follow Share @Utkarsh ,I think ur solution is correct..one another way is just divide numerator and denominator by n2 in both ( 2n2/3n2+1) and its power..and put n = ∞ ,it will become (2/3)0 =1 1 votes 1 votes Mk Utkarsh commented Mar 18, 2018 reply Follow Share ankitgupta yeah that's easier thanks i'll update the answer 1 votes 1 votes Please log in or register to add a comment.