AP EAMCET · Maths · Limits
If \(f(x)=\left(\frac{1+x}{1-x}\right)^{\frac{1}{x}}\) is continuous at \(x=0\) then \(f(0)=\)
- A \(e^{\frac{1}{2}}\)
- B \(e^2\)
- C \(e^{-2}\)
- D \(e^{\frac{-1}{2}}\)
Answer & Solution
Correct Answer
(B) \(e^2\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left(\frac{1+x}{1-x}\right)^{\frac{1}{x}}\) is continuous at \(x=0\) \(\Rightarrow f(0)=\lim _{x \rightarrow 0} f(x)\) Now, \(\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0}\left(\frac{1+x}{1-x}\right)^{\frac{1}{x}}\) ( \(1^{\infty}\) form)…
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 pairs of straight lines \(x^2-3 x y+2 y^2=0\) and \(x^2-3 x y+2 y^2+x-2=0\) form aAP EAMCET 2009 Hard
- \(\cos 36^{\circ}-\cos 72^{\circ}\) is equal toAP EAMCET 2012 Medium
- The area (in sq. units) of the region bounded by the curves \(y=4|\cos x|\) and \(y=-|\cos x|\) from \(x=-\frac{\pi}{2}\) to \(\frac{\pi}{2}\) isAP EAMCET 2023 Medium
- AP EAMCET 2021 Medium
- If \(\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}\) and \(\mathrm{g}: \mathbb{R} \rightarrow \mathbb{R}\) are defined by \(\mathrm{f}(\mathrm{x})=\mathrm{x}^3-\mathrm{x}\) and \(g(x)=\sin 2 x\), then the value of \(x \in(0,2 \pi)\) that satisfy \(\mathrm{f}(\mathrm{g}(\mathrm{x}))>0\), lie in the intervalAP EAMCET 2023 Medium
- An item is tested on a device for its defectiveness. The probability that such an item is defective is 0.3. The device gives accurate result in 8 out of 10 such tests. If the device reports that an item tested is not defective, then the probability that it is actually defective isAP EAMCET 2025 Medium
More PYQs from AP EAMCET
- Which of the following trigonometric values are negative?
\(\begin{aligned} & \text { I. } \sin \left(-292^{\circ}\right) \\ & \text { II. } \tan \left(-190^{\circ}\right) \\ & \text { III. } \cos \left(-207^{\circ}\right) \\ & \text { IV. } \cot \left(-222^{\circ}\right)\end{aligned}\)AP EAMCET 2022 Easy - What are the formal charges on terminal oxygens of ozone molecule?AP EAMCET 2023 Easy
- Identify the method of preparation of a colloidal sol from the followingAP EAMCET 2024 Easy
- The number of hydrogen bonds between guanine and cytosine; and between adenine and thymine in DNA isAP EAMCET 2013 Medium
- The coil of a moving coil galvanometer has an effective area of \(4 \times 10^{-2} \mathrm{~m}^2\). It is suspended in a magnetic field of \(5 \times 10^{-2} \mathrm{~Wb} \mathrm{~m}^{-2}\). If the deflection in the galvanometer coil is \(0.2 \mathrm{rad}\), when a current of \(5 \mathrm{~mA}\) is passed through it, thenAP EAMCET 2021 Medium
- In the circuit given below, if the bulb is to glow with maximum intensity, the value of ' \(R\) ' is
(neglect internal resistance of the cell)
AP EAMCET 2023 Medium