The system of equations:
x + y + z = 5
x + 2y + 3z = 9
x + 3y + λz = µ
has a unique solution, if
(a) λ = 5, µ = 13
(b) λ ≠ 5
(c) λ = 5, µ ≠ 13
(d) µ ≠ 13
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
f(x) = 3 + (x − 2)2/3 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) = [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
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
\[f\left( x \right) = \begin{cases}- 4x + 5, & 0 \leq x \leq 1 \\ 2x - 3, & 1 < x \leq 2\end{cases}\] 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
\[\frac{y}{x}\cos\left( \frac{y}{x} \right) dx - \left\{ \frac{x}{y}\sin\left( \frac{y}{x} \right) + \cos\left( \frac{y}{x} \right) \right\} dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[xy \log\left( \frac{x}{y} \right) dx + \left\{ y^2 - x^2 \log\left( \frac{x}{y} \right) \right\} dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( 1 + e^{x/y} \right) dx + e^{x/y} \left( 1 - \frac{x}{y} \right) dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( x^2 + y^2 \right)\frac{dy}{dx} = 8 x^2 - 3xy + 2 y^2\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
(x2 − 2xy) dy + (x2 − 3xy + 2y2) dx = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x\frac{dy}{dx} = y - x \cos^2 \left( \frac{y}{x} \right)\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x\frac{dy}{dx} - y = 2\sqrt{y^2 - x^2}\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x \cos\left( \frac{y}{x} \right) \cdot \left( y dx + x dy \right) = y \sin\left( \frac{y}{x} \right) \cdot \left( x dy - y dx \right)\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
(x2 + 3xy + y2) dx − x2 dy = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( x - y \right)\frac{dy}{dx} = x + 2y\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
(2x2 y + y3) dx + (xy2 − 3x3) dy = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x\frac{dy}{dx} - y + x \sin\left( \frac{y}{x} \right) = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[y dx + \left\{ x \log\left( \frac{y}{x} \right) \right\} dy - 2x dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
