COMEDK · Maths · 16. Limits
The value of \(\lim _\limits{x \rightarrow \infty}\left(\dfrac{x^2-2 x+1}{x^2-4 x+2}\right)^{2 x}\) is
- A \(e^2\)
- B \(e^{16}\)
- C \(e\)
- D \(e^4\)
Answer & Solution
Correct Answer
(D) \(e^4\)
Step-by-step Solution
Detailed explanation
The limit is of the form \(1^{\infty}\) as \(x \rightarrow \infty\). Let \(L = \lim_{x \rightarrow \infty} \left(\dfrac{x^2-2x+1}{x^2-4x+2}\right)^{2x}\). Using the formula \(\lim_{x \rightarrow a} [f(x)]^{g(x)} = e^{\lim_{x \rightarrow a} g(x)[f(x)-1]}\), we have:…
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
- \(A\) and \(B\) are invertible matrices of the same order such that \(\left|(A B)^{-1}\right|=8\) if \(|A|=2\) then \(|B|\) isCOMEDK 2023 Easy
- The circles \(a x^{2}+a y^{2}+2 g_{1} x+2 f_{1} y+c_{1}=0\) and \(b x^{2}+b y^{2}+2 g_{2} x+2 f_{2} y+c_{2}=0\) \((a \neq 0\) and \(b \neq 0)\) cut orthogonally ifCOMEDK 2016 Medium
- The maximum area in square units of an isosceles triangle inscribed in an ellipses \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) with its vertex at one end of the major axis isCOMEDK 2015 Hard
- If the area of region bounded by the lines \(y=2 x+1, x\)-axis, \(x=a\) and \(x=3\) is 10 sq units. Then the value of ' \(a\) ' isCOMEDK 2025 Medium
- If \({ }^{35} \mathrm{C}_{x+7}={ }^{35} \mathrm{C}_{4 x-2}\), then the values of \(x\) are eitherCOMEDK 2025 Easy
- If the lines \(x+3 y-9=0,4 x+b y-2=0\) and \(2 x-y-4=0\) are concurrent, then \(b=\)COMEDK 2016 Easy
More PYQs from COMEDK
- Identify the Carbonyl compound which will not be formed when hydration of Alkynes is carried out with dil. \(\mathrm{H}_2 \mathrm{SO}_4 / \mathrm{Hg}^{2+}\) at 333 K .
Acetone, Butanal, Ethanal, Butanone.COMEDK 2025 Medium - An endothermic reaction, \(A \rightarrow B\) has an activation energy as \(x \mathrm{~kJ} / \mathrm{mol}\). If the energy change of the reaction is \(y \mathrm{~kJ}\), the activation energy of the reverse reaction isCOMEDK 2014 Medium
- Which one of the following coordination entity is chiral?COMEDK 2015 Hard
- Name of the gas that can readily decolourise acidified \(\mathrm{KMnO}_4\) solution isCOMEDK 2024 Medium
- The sum of three numbers is 6 .
Twice the third number, when added to the first number gives 7 ,
On adding the sum of the second and third numbers to thrice the first number, we get 12 .
The above situation can be represented in matrix form as \(A X=B\).
Then the \(|\operatorname{adj} A|\) is equal toCOMEDK 2025 Medium - An air bubble in water \(\left(\mu=\dfrac{4}{3}\right)\) is shown in figure. The apparent depth of the image of the bubble in plane mirror viewed by observer is.
COMEDK 2023 Medium