TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow 2}\left[\left(x^2-4 x+4\right) \cos \left(\frac{2}{x-2}\right)+\frac{x^2-4}{x^3-2 x-4}\right]=\)
- A 0
- B \(\infty\)
- C 1
- D \(\frac{2}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{2}{5}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{x \rightarrow 2}\left[\left(x^2-4 x+4\right) \cos \left(\frac{2}{x-2}\right)+\frac{x^2-4}{x^3-2 x-4}\right] \\ & \Rightarrow \lim _{x \rightarrow 2}\left(x^2-4 x+4\right) \cos \left(\frac{2}{x-2}\right)+\lim _{x \rightarrow 2} \frac{x^2-4}{x^3-2 x-4} \\…
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
- If the two lines and are perpendicular, then the distance of their point of intersection from the point isTS EAMCET 2021 Easy
- If and , thenTS EAMCET 2020 Easy
- A certain question paper contains three parts \(A, B, C\) with four questions in part \(A\), five questions in part \(B\) and six questions in part \(C\). A student is required to answer seven questions choosing at least two questions from each part. Then the total number of different ways a student can choose his seven questions for answering, isTS EAMCET 2020 Medium
- If the tangent drawn at a point \(\mathrm{P}(t)\) on the hyperbola \(x^2-y^2=c^2\) cuts \(X\)-axis at T and the normal drawn at the same point \(P\) cuts the Y -axis at N , then the equation of the locus of the midpoint of TN isTS EAMCET 2024 Medium
- Two families of lines are given by \(a x+b y+c=0\) and \(4 a^2+9 b^2-c^2-12 a b=0\). Then the line common to both the families isTS EAMCET 2025 Medium
- The positive value of 'a' for which the system of linear homogeneous equations \(x+a y+z=0, a x+2 y-z=0,2 x+3 y+z=0\) has non-trivial solutions isTS EAMCET 2025 Medium
More PYQs from TS EAMCET
- A piece of copper and a piece of germanium are cooled from room temperature to \(80 \mathrm{~K}\). Then, which one of the following is correct?TS EAMCET 2017 Easy
- A block is placed on a parabolic shape ramp given by equation . If the coefficient of static friction is , then what is the maximum height above the ground at which the block can be placed without slipping?TS EAMCET 2022 Medium
- A message signal of frequency \(50 / \pi \mathrm{kHz}\) and peak voltage of \(5 \mathrm{~V}\) is used to modulate a carrier of frequency \(1 \mathrm{MHz}\) and peak voltage \(20 \mathrm{~V}\). The modulation index isTS EAMCET 2020 Easy
- Let \(x+y=k\) be a normal to the parabola \(y^2=12 x\). If \(p\) is length of the perpendicular from the focus of the parabola onto this normal, then \(4 k-2 p^2\) is equal toTS EAMCET 2012 Medium
- If and , thenTS EAMCET 2021 Medium
- If , thenTS EAMCET 2019 Medium