TS EAMCET · Maths · Differentiation
Let \(f(x)=\sin x, g(x)=\cos x, h(x)=x^2\) then \(\lim _{x \rightarrow 1} \frac{f(g(h(x)))-f(g(h(1)))}{x-1}=\)
- A 0
- B \(-2 \sin 1 \cos (\cos 1)\)
- C \(\infty\)
- D \(-2 \sin 1 \cos 1\)
Answer & Solution
Correct Answer
(B) \(-2 \sin 1 \cos (\cos 1)\)
Step-by-step Solution
Detailed explanation
Given \(f(x)=\sin x, g(x)=\cos x, h(x)=x^2\) \[ \lim _{x \rightarrow 1} \frac{f(g(h(x)))-f(g(h(1)))}{x-1}=\lim _{x \rightarrow 1} \frac{\sin \left(\cos x^2\right)-\sin (\cos 1)}{x-1} \] If Apply limit it gives \(\frac{0}{0}\) form, then apply L'Hospital rule.…
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
- \(\int \frac{\left(1-4 \sin ^2 x\right) \cos x}{\cos (3 x+2)} d x=\)TS EAMCET 2024 Hard
- The area (in square unit) of the circle which touches the lines \(4 x+3 y=15\) and \(4 x+3 y=5\) isTS EAMCET 2009 Easy
- The differential equation representing the family of circles of constant radius \(r\) isTS EAMCET 2019 Easy
- \(\vec{a}, \vec{b}, \vec{c}\) are non-coplanar vectors. If the three points \(\lambda \vec{a}-2 \vec{b}+c, 2 \vec{a}+\lambda \vec{b}-2 \vec{c}, 4 \dot{a}+7 \vec{b}-8 \vec{c}\) are collinear, then \(\lambda=\)TS EAMCET 2024 Easy
- TS EAMCET 2021 Medium
- The number of ways of arranging all the letters of the word "SUNITHA" so that the vowels always occupy the first, middle and last places isTS EAMCET 2023 Medium
More PYQs from TS EAMCET
- Four \(4 \Omega\) resistors are connected together along the edges of a square. A \(12 \mathrm{~V}\) battery with internal resistance of \(2 \Omega\) is connected across a pair of the diagonally opposite corners of the square. The power dissipated in the circuit isTS EAMCET 2020 Easy
- The parametric equations of the ellipse whose foci are and eccentricity is , areTS EAMCET 2022 Easy
- Let \(\mathbf{a}=2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=-\hat{\mathbf{j}}+\hat{\mathbf{k}}\). If \(\mathbf{c}\) is a vector such that \(\mathbf{a} \cdot \mathbf{c}=|\mathbf{c}|,|\mathbf{c}-\mathbf{a}|=2 \sqrt{2}\) and the angle between \(\mathbf{a} \times \mathbf{b}\) and \(\mathbf{c}\) is \(\frac{\pi}{3}\), then \(|(\mathbf{a} \times \mathbf{b}) \times \mathbf{c}|=\)TS EAMCET 2020 Medium
- If the line \(l x+m y=1\) is a normal to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), then \(\frac{a^2}{l^2}-\frac{b^2}{m^2}\) is equal toTS EAMCET 2007 Hard
- Identify the set, in which X and Y are correctly matched.
TS EAMCET 2024 Medium - A body of mass is executing simple harmonic motion (SHM). Its displacement (in ) at time t given by Its maximum kinetic energy isTS EAMCET 2021 Medium