A particle moves along the curve y = x2 + 2x. At what point(s) on the curve are the x and y coordinates of the particle changing at the same rate?
[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
If y = 7x − x3 and x increases at the rate of 4 units per second, how fast is the slope of the curve changing when x = 2?
[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
A particle moves along the curve y = x3. Find the points on the curve at which the y-coordinate changes three times more rapidly than the x-coordinate.
[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
\[\frac{d^3 y}{d x^3} + \left( \frac{d^2 y}{d x^2} \right)^3 + \frac{dy}{dx} + 4y = \sin x\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Find an angle θ which increases twice as fast as its cosine ?
[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
(xy2 + x) dx + (y − x2y) dy = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\sqrt{1 - y^2} dx + \sqrt{1 - x^2} dx = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Find an angle θ whose rate of increase twice is twice the rate of decrease of its cosine ?
[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
\[\frac{d^2 y}{d x^2} = \left( \frac{dy}{dx} \right)^{2/3}\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[2\frac{d^2 y}{d x^2} + 3\sqrt{1 - \left( \frac{dy}{dx} \right)^2 - y} = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[5\frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2}\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[y = x\frac{dy}{dx} + a\sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[y = px + \sqrt{a^2 p^2 + b^2},\text{ where p} = \frac{dy}{dx}\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{d^2 y}{d x^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log\left( \frac{d^2 y}{d x^2} \right)\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( \frac{d^2 y}{d x^2} \right)^2 + \left( \frac{dy}{dx} \right)^2 = x \sin \left( \frac{d^2 y}{d x^2} \right)\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
(y'')2 + (y')3 + sin y = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
The top of a ladder 6 metres long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is 4 metres from the wall, it is sliding away from the wall at the rate of 0.5 m/sec. How fast is the top-sliding downwards at this instance?
How far is the foot from the wall when it and the top are moving at the same rate?
[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
\[\frac{d^2 y}{d x^2} + 5x\left( \frac{dy}{dx} \right) - 6y = \log x\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{d^3 y}{d x^3} + \frac{d^2 y}{d x^2} + \frac{dy}{dx} + y \sin y = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{dy}{dx} + e^y = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
