Explanation

• A bounded linear operator satisfies a uniform norm inequality.
• The constant C must be finite and independent of x.
• Every bounded linear operator between normed spaces is continuous.

Last verified on 14-11-2026

Explanation

The supremum is the least upper bound of a set.

Every element of (0, 5) is less than 5.

Although 5 is not included in the set, it is its supremum.

Last verified on 14-11-2026

Explanation

The cross product of two perpendicular unit vectors gives another unit vector.

In the standard right-handed coordinate system, i × j = k.

The result is perpendicular to both i and j.

Last verified on 14-11-2026

Explanation

The degree is the power of the highest-order derivative.

The highest-order derivative is the second derivative.

Its power is 3, so the degree is 3.

Last verified on 14-11-2026

Explanation

The standard linear form is dy/dx + Py = Q.

The integrating factor is e raised to the integral of P dx.

Here, P = 2, so the integrating factor is e²ˣ.

Last verified on 14-11-2026