Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions

A homogeneous differential equation of the form \[\frac{dx}{dy} = h\left( \frac{x}{y} \right)\] can be solved by making the substitution

Which of the following is a homogeneous differential equation?

Verify Rolle's theorem for the following function on the indicated interval f(x) = x² − 8x + 12 on [2, 6] ?

Verify Rolle's theorem for the following function on the indicated interval f(x) = x² − 4x + 3 on [1, 3] ?

Verify Rolle's theorem for the following function on the indicated interval f (x) = (x − 1) (x − 2)² on [1, 2] ?

Verify Rolle's theorem for the following function on the indicated interval  f (x) = x(x − 1)² on [0, 1] ?

Verify Rolle's theorem for the following function on the indicated interval  f (x) = (x² − 1) (x − 2) on [−1, 2] ?

Verify Rolle's theorem for the following function on the indicated interval   f (x) = x(x − 4)² on the interval [0, 4] ?

Verify Rolle's theorem for the following function on the indicated interval  f(x) = x(x −2)² on the interval [0, 2] ?

Verify Rolle's theorem for the following function on the indicated interval f (x) = x² + 5x + 6 on the interval [−3, −2]  ?

Verify Rolle's theorem for each of the following function on the indicated interval f (x) = cos 2 (x − π/4) on [0, π/2] ?

Verify Rolle's theorem for the following function on the indicated interval  f(x) = sin 2x on [0, π/2] ?

Verify Rolle's theorem for the following function on the indicated interval f(x) = cos 2x on [−π/4, π/4] ?

Verify Rolle's theorem for the following function on the indicated interval f(x) = e^x sin x on [0, π] ?

Verify Rolle's theorem for the following function on the indicated interval f(x) = e^x cos x on [−π/2, π/2] ?

Verify Rolle's theorem for the following function on the indicated interval  f(x) = cos 2x on [0, π] ?

Verify Rolle's theorem for the following function on the indicated interval f (x) = \[\frac{\sin x}{e^x}\] on 0 ≤ x ≤ π ?

Verify Rolle's theorem for the following function on the indicated interval f(x) = sin 3x on [0, π] ?

Verify Rolle's theorem for the following function on the indicated interval f (x) = \[{e^{1 - x}}^2\] on [−1, 1] ?

Verify Rolle's theorem for the following function on the indicated interval f (x) = log (x² + 2) − log 3 on [−1, 1] ?