1. Tardigrade
  2. Question
  3. Mathematics
  4. If y=1+x+(x2/2 !)+(x3/3 !)+ ldots . .+(xn/n !) then (d y/d x)+(xn/n !)=

Q. If $y=1+x+\frac{x^{2}}{2 !}+\frac{x^{3}}{3 !}+\ldots . .+\frac{x^{n}}{n !}$ then $\frac{d y}{d x}+\frac{x^{n}}{n !}=$

KCETKCET 2022 Report Error

Solution:

$y=1+x+\frac{x^{2}}{2 !}+\frac{x^{3}}{3 !}+\cdots+\frac{x^{n}}{n !}$
$\frac{d y}{d x}=0+1+\frac{2 x}{2 \times 1 !}+\frac{3 x^{2}}{3 \times 2 !}+\cdots+\frac{x^{n-1}}{(n-1) !}$
$\frac{d y}{d x}+\frac{x^{n}}{n !}=1+\frac{2 x}{2 \times 1 !}+\frac{3 x^{2}}{3 \times 2 !}+\cdots+\frac{x^{n-1}}{(n-1) !}+\frac{x^{n}}{n !}= y$

Questions from KCET 2022

1. It is observed that $23 x+17 y=1$ for some integers $x$ and $y$. Then $(x, y)=$

2. The sum of all the positive divisors of $180$ excluding $1$ and itself is

3. If $x+y+z=\pi$ then the value of $\begin{vmatrix}\sin (x+y+z) & \sin B & \cos z \\ -\sin B & 0 & \tan A \\ \cos (x+y) & -\tan A & 0\end{vmatrix}$ is

4. If the value of a third order determinant is $11 $ , then the value of the determinant formed by the cofactors will be

5. If $A=\begin{bmatrix}1 & -1 & 2 \\ 2 & 3 & 1 \\ 1 & -2 & 3\end{bmatrix}$ then $\text{adj}\left(A^{-1}\right)=$

Mathematics Most Viewed Questions

1. The solution of $\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is

WBJEE 2011 Differential Equations

2. The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is

COMEDK 2009 Differential Equations

3. $\int\frac{1}{\sin x\, \cos x}$ dx is equal to

KEAM 2016 Integrals

4. If $\begin{bmatrix}1&- \tan\theta \\ \tan \theta&1\end{bmatrix}\begin{bmatrix}1&\tan \theta \\ - \tan \theta &1\end{bmatrix}^{-1} = \begin{bmatrix}a&-b\\ b&a\end{bmatrix}$ then

COMEDK 2009 Matrices

5. The value of $ \int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx $ is

KEAM 2007 Integrals

Latest Updates