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Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

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f (x) = [x] for −1 ≤ x ≤ 1, where [x] denotes the greatest integer not exceeding x Discuss the applicability of Rolle's theorem for the following function on the indicated intervals ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

f (x) = sin \[\frac{1}{x}\] for −1 ≤ x ≤ 1 Discuss the applicability of Rolle's theorem for the following function on the indicated intervals ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

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f (x) = 2x2 − 5x + 3 on [1, 3] Discuss the applicability of Rolle's theorem for the following function on the indicated intervals ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

f (x) = x2/3 on [−1, 1] Discuss the applicability of Rolle's theorem for the following function on the indicated intervals ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
\[\int\sqrt{3 + 2x - x^2} \text{ dx}\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

\[f\left( x \right) = \begin{cases}- 4x + 5, & 0 \leq x \leq 1 \\ 2x - 3, & 1 < x \leq 2\end{cases}\] Discuss the applicability of Rolle's theorem for the following function on the indicated intervals ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
\[\int\sqrt{x^2 + x + 1} \text{ dx}\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\sqrt{x - x^2} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\sqrt{1 + x - 2 x^2} \text{ dx }\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\cos x \sqrt{4 - \sin^2 x}\text{ dx}\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int e^x \sqrt{e^{2x} + 1} \text{ dx}\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\sqrt{9 - x^2}\text{ dx}\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\sqrt{16 x^2 + 25} \text{ dx}\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\sqrt{4 x^2 - 5}\text{ dx}\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\sqrt{2 x^2 + 3x + 4} \text{ dx}\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Write a value of

\[\int\frac{1 + \cot x}{x + \log \sin x} \text{ dx }\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Write a value of

\[\int x^2 \sin x^3 \text{ dx }\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Write a value of

\[\int \tan^3 x \sec^2 x \text{ dx }\].

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Write a value of

\[\int e^x \left( \sin x + \cos x \right) \text{ dx}\]

 

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

Write a value of

\[\int \tan^6 x \sec^2 x \text{ dx }\] .
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
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