Question:
$ \lim_{π₯β\infty}(1+\frac{1}{x})$ is equal to
$ \lim_{π₯β\infty}(1+\frac{1}{x})$ is equal to
Updated On: Feb 10, 2025
- e
- 1/e
- 1
- $ \infty $
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Limit Definition of the Mathematical Constant e
This limit represents the definition of the mathematical constant e, which is the base of natural logarithms.
It describes the limit:
limx β β (1 + 1/x)x
As x approaches infinity, this expression is known to converge to e, a fundamental constant in mathematics.
Was this answer helpful?
0
0
Top Questions on Limits
- Match List-I with List-II:
\[\begin{array}{|c|c|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline \text{(A)}\ \lim_{x\to 0}(1+2x)^{\frac{1}{x}} & \text{(I)}\ e^{6} \\ \hline \text{(B)}\ \lim_{x\to \infty}\left(1+\frac{1}{x}\right)^{x} & \text{(II)}\ e^{2} \\ \hline \text{(C)}\ \lim_{x\to 0}(1+5x)^{\frac{2}{x}} & \text{(III)}\ e \\ \hline \text{(D)}\ \lim_{x\to \infty}\left(1+\frac{3}{x}\right)^{2x} & \text{(IV)}\ e^{5} \\ \hline \end{array}\] Choose the correct answer from the options given below: - The value of $\displaystyle \lim_{x \to \infty}\left(1+\frac{2}{3x}\right)^{x}$ is:
- Evaluate: \[ \lim_{x \to 0} \frac{\sin 3x - 3 \sin x}{x^3} \]
- Given below are two statements: Statement I: $\lim_{x \to 0} \left( \frac{\tan^{-1} x + \log_e \sqrt{\frac{1+x}{1-x}} - 2x}{x^5} \right) = \frac{2}{5}$ Statement II: $\lim_{x \to 1} \left( \frac{2}{x^{1-x}} \right) = \frac{1}{e^2}$ In the light of the above statements, choose the correct answer from the options given below
- For $ t>-1 $, let $ \alpha_t $ and $ \beta_t $ be the roots of the equation $ \left( (t + 2)^{\frac{1}{7}} - 1 \right)x^2 + \left( (t + 2)^{\frac{1}{6}} - 1 \right)x + \left( (t + 2)^{\frac{1}{21}} - 1 \right) = 0. $ If $ \lim_{t \to 1^+} \alpha_t = a $ and $ \lim_{t \to 1^+} \beta_t = b $, then $ 72(a + b)^2 $ is equal to:
View More Questions
Questions Asked in IIT JAM EN exam
- Consider the matrix \( A = \begin{bmatrix} 4 & -1 \\ 12 & -3 \end{bmatrix} \).
The value of the determinant of \( A^5 \) is .......... (rounded off to two decimal places).- IIT JAM EN - 2025
- Linear Algebra
The sum of the payoffs to the players in the Nash equilibrium of the following simultaneous game is ............
Player Y C NC Player X X: 50, Y: 50 X: 40, Y: 30 X: 30, Y: 40 X: 20, Y: 20 - IIT JAM EN - 2025
- Economics and economic theories
- Consider the economy described by the following: \[ Y = C + I + G \quad \text{with} \quad Y = 5000, \, G = 1000, \, T = 1000, \quad \text{and} \quad C = 250 + 0.75(Y - T), \] where \( Y \), \( C \), \( I \), \( G \), and \( T \) are national income, private consumption spending, investment expenditure, government expenditure, and tax revenue respectively. In this economy, private saving is ............
- IIT JAM EN - 2025
- Microeconomics
- Demand curve for a commodity in your consumption basket is given by \( P^2 Q^5 = 392.67 \). The absolute value of your own price elasticity of demand for this commodity is ........ (rounded off to one decimal place).
- IIT JAM EN - 2025
- Microeconomics
- Lerner Index (\( L \)), a measure of market power, is defined as \( L = \frac{P - MC}{P} \), where \( P \) and \( MC \) are, respectively, price and marginal cost of a firm. If a profit maximizing firm faces the demand curve \( P^2 Q = 7 \), the value of \( L \) is ............ (rounded off to one decimal place).
- IIT JAM EN - 2025
- Microeconomics
View More Questions