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If \[f\left( x \right) = \begin{cases}\frac{1 - \cos x}{x \sin x}, & x \neq 0 \\ \frac{1}{2} , & x = 0\end{cases}\]
then at x = 0, f (x) is
Chapter: [5] Continuity and Differentiability
Concept: undefined >> undefined
Concept: undefined >> undefined
\[s^2 \frac{d^2 t}{d s^2} + st\frac{dt}{ds} = s\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
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\[\frac{d^3 y}{d x^3} + \left( \frac{d^2 y}{d x^2} \right)^3 + \frac{dy}{dx} + 4y = \sin x\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
(xy2 + x) dx + (y − x2y) dy = 0
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\sqrt{1 - y^2} dx + \sqrt{1 - x^2} dx = 0\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{d^2 y}{d x^2} = \left( \frac{dy}{dx} \right)^{2/3}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[2\frac{d^2 y}{d x^2} + 3\sqrt{1 - \left( \frac{dy}{dx} \right)^2 - y} = 0\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[5\frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[y = x\frac{dy}{dx} + a\sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[y = px + \sqrt{a^2 p^2 + b^2},\text{ where p} = \frac{dy}{dx}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{d^2 y}{d x^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log\left( \frac{d^2 y}{d x^2} \right)\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\left( \frac{d^2 y}{d x^2} \right)^2 + \left( \frac{dy}{dx} \right)^2 = x \sin \left( \frac{d^2 y}{d x^2} \right)\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
(y'')2 + (y')3 + sin y = 0
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{d^2 y}{d x^2} + 5x\left( \frac{dy}{dx} \right) - 6y = \log x\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{d^3 y}{d x^3} + \frac{d^2 y}{d x^2} + \frac{dy}{dx} + y \sin y = 0\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx} + e^y = 0\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\left( \frac{dy}{dx} \right)^3 - 4 \left( \frac{dy}{dx} \right)^2 + 7y = \sin x\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[e^\frac{dy}{dx} = x + 1 ; y\left( 0 \right) = 3\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx} = \left( 1 + x^2 \right)\left( 1 + y^2 \right)\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
Define order of a differential equation.
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
