Question:
Evaluate the following limit :
\(\lim\limits_{x\rightarrow0}\frac{\text{ln}((x^2+1)\cos x)}{x^2}\) = ________.
Evaluate the following limit :
\(\lim\limits_{x\rightarrow0}\frac{\text{ln}((x^2+1)\cos x)}{x^2}\) = ________.
\(\lim\limits_{x\rightarrow0}\frac{\text{ln}((x^2+1)\cos x)}{x^2}\) = ________.
Updated On: Dec 16, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 0.5
Solution and Explanation
The correct answer is 0.5
Was this answer helpful?
0
2
Top Questions on Limits
- \(\lim\limits_{x→0} \frac {e^{|2sinx|}-2|sinx|-1}{x^2}\) is
- If the domain of the function \[f(x) = \frac{\sqrt{x^2 - 25}}{(4 - x^2)} + \log_{10}(x^2 + 2x - 15)\]is $(-\infty, \alpha) \cup [\beta, \infty)$, then $\alpha^2 + \beta^3$ is equal to:
- If \[ \alpha = \lim_{x \to 0^+} \left( \frac{e^{\sqrt{\tan x}} - e^{\sqrt{x}}}{\sqrt{\tan x} - \sqrt{x}} \right) \] \[ \beta = \lim_{x \to 0} (1 + \sin x)^{\frac{1}{2\cot x}} \] are the roots of the quadratic equation \(ax^2 + bx - \sqrt{e} = 0\), then \(12 \log_e (a + b)\) is equal to _________.
- If \[ \lim_{x \to 1} \frac{(5x+1)^{1/3} - (x+5)^{1/3}}{(2x+3)^{1/2} - (x+4)^{1/2}} = \frac{m \sqrt{5}}{n (2n)^{2/3}}, \] where \( \text{gcd}(m, n) = 1 \), then \( 8m + 12n \) is equal to _____
- The value of \[ \lim_{x \to 0} 2 \left( \frac{1 - \cos x \sqrt{\cos 2x} \, \sqrt[3]{\cos 3x} \ldots \sqrt[10]{\cos 10x}}{x^2} \right) \] is _____.
View More Questions
Questions Asked in GATE AR exam
- Two fair coins are tossed independently. X is a random variable that takes a value of 1 if both tosses are heads and 0 otherwise. Y is a random variable that takes a value of 1 if at least one of the tosses is heads and 0 otherwise.
The value of the covariance of X and Y is _________ (rounded off to three decimal places).- GATE AR - 2024
- Random variables
- For the beam shown below, ignoring the self-weight, the maximum hogging moment (in kN·m) generated for the loads indicated is _______ (rounded off to one decimal place).
- GATE AR - 2024
- High Rise and Long Span structures, gravity and lateral load resisting systems
- Consider the following tree traversals on a full binary tree :
(i) Preorder
(ii) Inorder
(iii) Postorder
Which of the following traversal options is/are sufficient to uniquely reconstruct the full binary tree ?- GATE AR - 2024
- Representation of Binary Tree
- Consider the 3 × 3 matrix M = \(\begin{bmatrix} 1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6 \end{bmatrix}.\)
The determinant of (M2 + 12M) is ________. - Consider the following sorting algorithms:
(i) Bubble sort
(ii) Insertion sort
(iii) Selection sort
Which ONE among the following choices of sorting algorithms sorts the numbers in the array [4, 3, 2, 1, 5] in increasing order after exactly two passes over the array ?- GATE AR - 2024
- Sorting
View More Questions