MHT CET · Maths · Limits
\(\lim _{x \rightarrow 2}(x-1)^{\frac{1}{3 x-6}}=\)
- A \(\mathrm{e}^2\)
- B \(\mathrm{e}^3\)
- C \(\mathrm{e}^{\frac{1}{3}}\)
- D \(\mathrm{e}^{\frac{1}{2}}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{e}^{\frac{1}{3}}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \lim _{x \rightarrow 2}(x-1)^{\frac{1}{3 x-6}} \\ & =\lim _{x \rightarrow 2}(x-2+1)^{\frac{1}{3(x-2)}}=\lim _{x \rightarrow 2}\left\{[1+(x-2)]^{\frac{1}{(x-2)}}\right\}^{\frac{1}{3}}=e^{\frac{1}{3}}\end{aligned}\)
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 graphical solution set of the system of inequations \(2 x+3 y \leq 6, x+4 y \geq 4, x \geq 0, y \geq 0\) is given by
MHT CET 2024 Easy - The maximum value of isMHT CET 2017 Easy
- In a triangle ABC , with usual notations , \(\tan \left(\frac{\mathrm{A}}{2}\right)=\frac{5}{6}, \tan \left(\frac{\mathrm{C}}{2}\right)=\frac{2}{5}\), thenMHT CET 2025 Medium
- If \(\sin ^2 x+\cos ^2 y=1\), then \(\frac{d y}{d x}=\)MHT CET 2021 Medium
- If \(\int \frac{d \theta}{\cos ^2 \theta(\tan 2 \theta+\sec 2 \theta)}=\lambda \tan \theta+2 \log |f(\theta)|+c\)
where \(\mathrm{C}\) is a constant of integration, then the ordered pair \((\lambda, f(\theta))\) is equal toMHT CET 2022 Hard - If \(0 \leqslant x \leqslant \pi\) and \(81^{\sin ^2 x}+81^{\cos ^2 x}=30\)
Then \(x\) takes the valueMHT CET 2025 Medium
More PYQs from MHT CET
- A particle is displaced from point \(\mathrm{P}(3 \mathrm{~m}, 4 \mathrm{~m}, 5 \mathrm{~m})\) to a point \(Q(2 m, 3 m, 4 m)\) under a constant force \(\vec{F}=(3 \hat{i}+4 \hat{j}+5 \hat{k}) N\). The work done by the force in this process isMHT CET 2025 Easy
- The equivalent statement of " If three vertices of a triangle are represented by cube roots of unity, then the triangle is an equilateral triangle " isMHT CET 2025 Easy
- The rate law equation for a reaction between \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) is \(\mathrm{r}=\mathrm{k}[\mathrm{A}][\mathrm{B}][\mathrm{C}]^2\), what will be new rate of reaction if concentration of both A and B are doubled.MHT CET 2021 Medium
- The solution of the differential equation \(\left(1+e^{-x}\right)\left(1+y^2\right) \frac{d y}{d x}=y^2\) which passes through the point \((0,1)\) isMHT CET 2022 Medium
- The sum of the magnitudes of two vectors \(\vec{A}\) and \(\vec{B}\) is 8 and magnitude of the resultant is 4. If the resultant vector is perpendicular to any one vector, then the magnitudes of the two vectors \(\vec{A}\) and \(\vec{B}\) areMHT CET 2020 Easy
- The shortest distance between the lines \(\quad \bar{r}=(1-t) \hat{\imath}+(t-2) \hat{\jmath}+(3-2 t) \hat{k}\) and
\(\bar{r}=(p+1) \hat{\imath}+(2 p-1) \hat{\jmath}+(2 p+1) \hat{k} \quad\) isMHT CET 2020 Easy