Evaluate the following limit :
\(\lim\limits_{x\rightarrow0}\frac{\text{ln}((x^2+1)\cos x)}{x^2}\) = ________.
\(\lim\limits_{x\rightarrow0}\frac{\text{ln}((x^2+1)\cos x)}{x^2}\) = ________.
Top Questions on Limits
- Evaluate the limit $ \lim_{n \to \infty} \frac{6^n - 9x - 7^n + 1}{\sqrt{2} - \sqrt{11} + \cos n} $
- The limit of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:
- Evaluate: \[ \lim_{x \to 0} \frac{\sin 3x - 3 \sin x}{x^3} \]
- BITSAT - 2025
- Mathematics
- Limits
- Let \( \Gamma \) be the curve \( y = b e^{-x/a} \) and \( L \) be the straight line:
\[ \frac{x}{a} + \frac{y}{b} = 1, \quad a, b \in \mathbb{R}. \]
Then:- WBJEE - 2024
- Mathematics
- Limits
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Questions Asked in GATE AR exam
A four-arm uncontrolled un-signaled urban intersection of both-way traffic is illustrated in the figure. Vehicles approaching the intersection from the directions A, B, C, and D can move to either left, right, or continue in straight direction. No U-turn is allowed. In the given situation, the maximum number of vehicular crossing conflict points for this intersection is _________ (answer in integer)
- GATE AR - 2025
- Traffic survey methods, Traffic flow Analysis
An individual chooses a transport mode for a particular trip based on three attributes i.e., cost of journey (X), In-vehicle travel time to reach destination (Y), and Out-of-vehicle time taken to access mode at respective stops (Z). The values for these attributes for three modes Rail, Bus and Para-transit are given in the table. If the general utility (U) equation is \( U = - 0.5 \times X - 0.3 \times Y - 0.4 \times Z \), using the Logit model, the estimated probability of choosing Bus is _________ (rounded off to two decimal places).
- GATE AR - 2025
- Transportation