AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow 1}\left(\lim _{7 \rightarrow \infty} y\left((e x)^{1 / y}-1\right)\right)=\)
- A \(\mathrm{e}\)
- B 0
- C 1
- D \(-1\)
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & =\lim _{x \rightarrow 1}\left(\lim _{y \rightarrow \infty} y\left(1+\frac{(x / y)}{1 !}+\frac{(x / y)^2}{2 !}+\frac{(x / y)^3}{3 !}+\ldots-1\right)\right) \\ & =\lim _{x \rightarrow 1}(x+0)=1+0=1 .\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The difference between the absolute maximum and absolute minimum values of the function \(f(x)=2 x^3-15 x^2+36 x-30\) on \([-1,4]\) isAP EAMCET 2025 Medium
- \(\int e^{x / 2}\left(\frac{2+\sin x}{1+\cos x}\right) d x=\)AP EAMCET 2020 Hard
- \(\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}\) is equal toAP EAMCET 2010 Easy
- Equation of the directrix of the parabola whose focus is and the tangent at the vertex is isAP EAMCET 2022 Easy
- \(\int \frac{d x}{\sin x+\sin 2 x}=\)AP EAMCET 2019 Medium
- If \(x=4 \cos ^3 \theta\) and \(y=3 \sin ^2 \theta\), then \(\frac{d^2 y}{d x^2}\) at \(\theta=\frac{\pi}{4}\), isAP EAMCET 2019 Medium
More PYQs from AP EAMCET
- Which one of the following indicates correct order of atomic size of the given elements?AP EAMCET 2023 Easy
- If \(4 x-3 y-5=0\) is a normal to the ellipse \(3 x^2+8 y^2=k\), then the equation of the tangent drawn to this ellipse at the point \((-2, m)(m\gt0)\) isAP EAMCET 2024 Easy
- The point of concurrence of all conjugate lines of the line \(5 x+7 y-78=0\) with respect to the circle \(x^2+y^2+6 x+8 y-96=0\) isAP EAMCET 2019 Hard
- The speed of a particle changes from \(\sqrt{5} \mathrm{~ms}^{-1}\) to \(2 \sqrt{5} \mathrm{~ms}^{-1}\) in a time \(t\). If the magnitude of change in its velocity is \(5 \mathrm{~ms}^{-1}\), the angle between the initial and final velocities of the particle isAP EAMCET 2019 Easy
- If three points \(A, B\) and \(C\) have position vectors \((1, x, 3),(3,4,7)\) and \((y,-2,-5)\) respectively and if they are collinear, then \((x, y)\) isAP EAMCET 2002 Easy
- If \(\mathbf{a}\) is a vector of magnitude \(7, \mathbf{b}\) is a vector of magnitude 8 , then the maximum value of \(\mathbf|{a} \cdot \mathbf{b}|\) isAP EAMCET 2021 Easy