_ n _ r = 1 ^n 1 n e^ r n is - Vidyadip

MCQ

$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {\frac{1}{n}{e^{\frac{r}{n}}}} $ is

A
$e + 1$
✓
$e - 1$
C
$1 - e$
D
$e$

✓

Answer

Correct option: B.

$e - 1$

b
(b) $\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {\frac{1}{n}{e^{\frac{r}{n}}} = \int_0^1 {{e^x}dx = [{e^x}]_0^1 = e - 1} } $.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $a_1=1, a_2, a_3, a_4, \ldots$. be consecutive natural numbers. Then $\tan ^{-1}\left(\frac{1}{1+ a _1 a _2}\right)+\tan ^{-1}\left(\frac{1}{1+ a _2 a _3}\right)$ $+\ldots . .+\tan ^{-1}\left(\frac{1}{1+ a _{2021} a _{2022}}\right)$ is equal to

Let $R$ be a relation on the set $N$ be defined by $\{(x, y)| x, y \in N, 2x + y = 41\}$. Then $R$ is

The void relation on a set $A$ is

Area of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is

Choose the correct answer from the given four options. If $A $ is a square matrix such that $A^2 = I,$ then $(A - I)^3 + (A + I)^3 - 7A$ is equal to:

Let $\quad f:(-\infty, \infty)-\{0\} \rightarrow R$ be a differentiable function such that $f^{\prime}(1)=\lim _{a \rightarrow \infty} a^2 f\left(\frac{1}{a}\right)$.

Then $\lim _{a \rightarrow \infty} \frac{a(a+1)}{2} \tan ^{-1}\left(\frac{1}{a}\right)+a^2-2 \log _e a$ is equal to

Find adjoint of each of the matrices $\left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 3 & 5 \\ -2 & 0 & 1\end{array}\right]$

Let $x_{0}$ be the point of local maxima of $f(x)=\vec{a} \cdot(\vec{b} \times \vec{c}),$ where $\vec{a}=x \hat{i}-2 \hat{j}+3 \hat{k}$ $\overrightarrow{ b }=-2 \hat{ i }+ x \hat{ j }-\hat{ k }$ and $\overrightarrow{ c }=7 \hat{ i }-2 \hat{ j }+ x \hat{ k } \cdot$ Then the value of $\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}$ at $x=x_{0}$ is

Choose the correct answer from the given four options. In a college, $30\%$ students fail in physics, $25\%$ fail in mathematics and $10\% $ fail in both. One student is chosen at random. The probability that she fails in physics if she has failed in mathematics is :

$\int_{}^{} {{{\sec }^p}x\tan x\;dx = } $