lim _{n rightarrow infty} Pleft(1+frac{r}{100 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $y = \lim _{n \rightarrow \infty} P\left(1+\frac{r}{100 n}\right)^{t n}$.We know the standard limit formula $\lim _{k \rightarrow \infty} (1+\

Vedclass · Accepted Answer

$P e^{\frac{r t}{100}}$

Vedclass · Answer

(C) Let $y = \lim _{n \rightarrow \infty} P\left(1+\frac{r}{100 n}\right)^{t n}$.We know the standard limit formula $\lim _{k \rightarrow \infty} (1+\frac{x}{k})^k = e^x$.Here,let $k = n$. Then the expression becomes $P \left[ \lim _{n \rightarrow \infty} (1+\frac{r/100}{n})^n \right]^t$.Using the limit formula,$\lim _{n \rightarrow \infty} (1+\frac{r/100}{n})^n = e^{r/100}$.Therefore,$y = P \left( e^{r/100} \right)^t = P e^{\frac{rt}{100}}$.

$\lim _{n \rightarrow \infty} P\left(1+\frac{r}{100 n}\right)^{t n} =$

Similar Questions

$\lim _{x \rightarrow 0} \frac{\tan 2x - 2\tan x}{(1 - \cos x)(2^x - 1)} = $

Let $[P]$ denote the greatest integer $\leq P$. If $0 \leq a \leq 2$,then the number of integral values of $a$ such that $\lim _{x \rightarrow a}([x^2]-[x]^2)$ does not exist is:

Let for all $x > 0$,$f(x) = \lim_{n \rightarrow \infty} n(x^{1/n} - 1)$,then

$\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^3}$ equals

Find the limit: $\mathop {\lim }\limits_{x \to 3} [x(x+1)]$

Vedclass Test Series

Exam Paper Generator

Online Exam Module