TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0} \frac{\sqrt{\cos x}-\sqrt[3]{\cos x}}{\sin ^2 x}=\)
- A \(\frac{1}{2}\)
- B \(-\frac{1}{12}\)
- C \(-\frac{1}{6}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(B) \(-\frac{1}{12}\)
Step-by-step Solution
Detailed explanation
\( \lim _{x \rightarrow 0} \frac{\frac{d}{dx}(\cos^{1/2} x - \cos^{1/3} x)}{\frac{d}{dx}(\sin ^2 x)} \) \( = \lim _{x \rightarrow 0} \frac{-\frac{1}{2}\sin x (\cos x)^{-1/2} + \frac{1}{3}\sin x (\cos x)^{-2/3}}{2\sin x \cos x} \)…
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
- \(\int \frac{d x}{(1+x) \sqrt{8+7 x-x^2}}=\)TS EAMCET 2019 Medium
- If each root of the equation \(2 x^3+a x^2-8 x+b=0\) is reduced by one, then in the transformed equation thus formed, the term containing \(x^2\) and the constant term are vanishing. The roots of the original equation areTS EAMCET 2019 Medium
- If \(C_1\) and \(C_2\) are the centres of similitude with respect to the circles \(x^2+y^2+6 x+8 y+24=0\) and \(x^2+y^2-6 x-8 y\) \(+9=0\) then \(C_1 C_2=\)TS EAMCET 2022 Medium
- If two cards are drawn one after the other without replacement from a well-shuffled ordinary deck of cards, then the probability that both of them are aces isTS EAMCET 2021 Easy
- If the area lying in the first quadrant and bounded by the circle \(x^2+y^2-4 x=0\), the parabola \(y^2=x\) and the \(X\)-axis is \(A\), then \(6 A-9 \sqrt{3}=\)TS EAMCET 2020 Easy
-
The correct match is
TS EAMCET 2019 Medium
More PYQs from TS EAMCET
- If the coefficient of in the expansion of is equal to the coefficient of in the expansion of , thenTS EAMCET 2018 Hard
- Identify the element for which +1 oxidation state is more stable than +3 oxidation stateTS EAMCET 2024 Easy
- If \(s\) and \(p\) are respectively the sum and the product of the slopes of the lines \(3 x^2-2 x y-15 y^2=0\), then \(s: p\) is equal toTS EAMCET 2011 Easy
- In the Millikan's oil drop method, which of the following force does not act on the oil drop?TS EAMCET 2019 Easy
- Suppose \(\alpha, \beta, \gamma\) are the roots of \(x^3+x^2+x+2=0\). Then, the value of \(\left(\frac{\alpha+\beta-2 \gamma}{\gamma}\right)\left(\frac{\beta+\gamma-2 \alpha}{\alpha}\right)\left(\frac{\gamma+\alpha-2 \beta}{\beta}\right)\) isTS EAMCET 2015 Easy
- Which of the following sets of functional groups is meta-directing group?TS EAMCET 2020 Medium