Calculus for JEE (Standard)

Calculus for JEE: core idea

• 1. Chain: $\dfrac{d}{dx}e^{3x}$ at $0$?

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• 2. $\int_0^1 xe^{x}\,dx$?

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• 3. Tangent to $y=x^2$ at $1$: slope?

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• 4. Max of $-x^2+4x$?

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• 5. $\int_0^{\pi}\sin x\,dx$?

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• 6. MVT: $f(x)=x^2$ on $[1,3]$: $c$ where $f'(c)=4$?

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• 7. Area between $y=x$ and $y=x^2$ on $[0,1]$?

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• 8. $\int_1^{\infty}1/x^2\,dx$?

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• 9. Critical points of $x^3-3x$: product of them?

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