If \(lim_{x\rightarrow 0} \frac{\sqrt 1 + \sqrt{1+x^4}-\sqrt 2}{x^4}=A\) and \(lim_{x \rightarrow 0} \frac{sin^2x}{\sqrt 2 - \sqrt{1+cosx}}=B\), then \(AB^3\) = ____.
- 8
- 32
- 6
- None of these
The Correct Option is B
Solution and Explanation
The correct option is (B): \(32\)
Top Questions on Limits
- $ \lim_{𝑥→\infty}(1+\frac{1}{x})$ is equal to
- Let \(k\in R\). If \(\)\(\)\(\)\(\lim\limits_{x→0+}(\sin(\sin kx)+\cos x+x)^{\frac{2}{x}}=e^6\), then the value of k is
- Let S be the set of all \((α, β) ∈ \R\times\R\) such that
\(\lim\limits_{x\rightarrow\infin}\frac{\sin(x^2)(\log_ex)^\alpha\sin(\frac{1}{x^2})}{x^{αβ}(\log_e(1+x))^β}=0\)
Then which of the following is (are) correct ? - \(\lim\limits_{x→0} \frac {e^{|2sinx|}-2|sinx|-1}{x^2}\) is
- Evaluate the following limit :
\(\lim\limits_{x\rightarrow0}\frac{\text{ln}((x^2+1)\cos x)}{x^2}\) = ________.
Questions Asked in JEE Main exam
- Find the acceleration of \(2\) \(kg\) block shown in the diagram (neglect friction)
- JEE Main - 2024
- Acceleration
- If \(|2A|^3 =21\) and \(\begin{bmatrix} 1 & 0 & 0 \\[0.3em] 0 & α & β \\[0.3em] 0 & β & α \end{bmatrix}\), then a is (if \(α,β∈I\))
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- Matrices
- Let \(α\) and \(β\) the roots of equation \(px^2 + qx - r = 0\), where \(P≠ 0\). If \(p,q,r\) be the consecutive term of non constant G.P and \(\frac{1}{α} + \frac{1}{β} = \frac{3}{4}\) then the value of \((α - β)^2\) is:
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- Geometric Progression
- Two lines \(L_1 \;\& \;L_2\) passing through origin trisecting the line segment intercepted by the line \(4x + 5y = 20\) between the coordinate axes. Then the tangent of angle between the lines \(L_1\) and \(L_2\) is
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- Tangents and Normals
- Rank of the word 'GTWENTY' in dictionary is _____ .
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- permutations and combinations
Concepts Used:
Limits
A function's limit is a number that a function reaches when its independent variable comes to a certain value. The value (say a) to which the function f(x) approaches casually as the independent variable x approaches casually a given value "A" denoted as f(x) = A.
If limx→a- f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the left of ‘a’. This value is also called the left-hand limit of ‘f’ at a.
If limx→a+ f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the right of ‘a’. This value is also called the right-hand limit of f(x) at a.
If the right-hand and left-hand limits concur, then it is referred to as a common value as the limit of f(x) at x = a and denote it by lim x→a f(x).
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