COMEDK · Maths · 16. Limits
\(\lim\limits_{x \to \frac{\pi}{2}}\left(\dfrac{1 - \sin x}{\cos x}\right)\) is equal to
- A \(-1\)
- B \(1\)
- C \(\dfrac{1}{2}\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
The given limit is of the form \(\dfrac{0}{0}\) as \(x \to \dfrac{\pi}{2}\). Multiplying the numerator and the denominator by \(1 + \sin x\): \(\lim_{x \to \dfrac{\pi}{2}} \left( \dfrac{1 - \sin x}{\cos x} \times \dfrac{1 + \sin x}{1 + \sin x} \right)\)…
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 events A and B are mutually exclusive events such that \(P(A)=\dfrac{1}{3}(3 x+1)\) and \(P(B)=\dfrac{1}{4}(1-x)\) then the possible values of \(x\) lies in the intervalCOMEDK 2024 Medium
- \(\text { If } y=\sin ^{-1}\left(\dfrac{5 x+12 \sqrt{1-x^2}}{13}\right) \text { then } \dfrac{d y}{d x} \text { equals }\)COMEDK 2024 Medium
- If \(A=\left[\begin{array}{cc}k+1 & 2 \\ 4 & k-1\end{array}\right]\) is a singular matrix, then possible values of \(\mathrm{k}\) areCOMEDK 2023 Easy
- The solution of the differential equation \(e^{-x}(y+1) d y+\left(\cos ^{2} x-\sin 2 x\right) y(d x)=0\) subjected to the condition that \(y=1\), when \(x=0\) isCOMEDK 2016 Hard
- Let \(M\) be the set of all \(2 \times 2\) matrices with entries from the set R of real numbers. Then the function \(f: M \rightarrow R\) defined by \(f(A)=|A|\) for every \(A \in M\) isCOMEDK 2025 Medium
- The derivative of \(y = \sin^2\left[\cot^{-1}\left(\sqrt{\dfrac{1-x}{1+x}}\right)\right]\) isCOMEDK 2026 Medium
More PYQs from COMEDK
- The time required for \(100 \%\) completion of zero order reaction isCOMEDK 2012 Easy
- Which of the following chemicals does not liberate hydrogen gas on reaction with aluminium metal?COMEDK 2015 Hard
- During the formation of a chemical bondCOMEDK 2020 Medium
- \(\mathrm{Ti}^{2+}\) is purple while \(\mathrm{Ti}^{4+}\) is colourless becauseCOMEDK 2023 Medium
- A convex lens forms a real image of an object with magnification \(m_1\). The lens is moved towards the object to obtain another real image of magnification \(\mathrm{m}_2\). The image distance is increased by x . The focal length of the lens isCOMEDK 2025 Medium
- The inclination of a straight line passing through the point \((-3,6)\) and the midpoint of the line joining the points \((4,-5)\) and \((-2,9)\) isCOMEDK 2025 Easy