Q1
A function $f(x)$ is continuous at $x = a$ if:
📝 SolutionA function is continuous at $x = a$ when the limit as $x \to a$ exists and equals $f(a)$.
Q2
The derivative of $x^n$ with respect to $x$ is:
📝 SolutionBy the power rule, $\frac{d}{dx}(x^n) = nx^{n-1}$.
Q3
The derivative of $\sin x$ is:
📝 Solution$\frac{d}{dx}(\sin x) = \cos x$.
Q4
The derivative of a constant is:
📝 SolutionThe derivative of any constant is 0, since a constant does not change.
Q5
The derivative of $e^x$ is:
📝 SolutionThe exponential function $e^x$ is its own derivative: $\frac{d}{dx}(e^x) = e^x$.
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Class 12 · Maths
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