Explanation

The Fourier series expansion of an even, periodic function contains only cosine terms and a constant term.

In other words, the sine terms are absent.

Even functions:

An even function is symmetric about the y-axis, meaning f(x) = f(-x). 

Fourier series:

A Fourier series represents a periodic function as a sum of sine and cosine waves. 

Explanation

If one root of the equation is 2, then we can factor the left-hand side of the equation as (x - 2)(x^2 - 4x + 3) = (x - 2)(x - 1)(x - 3) = 0.

This tells us that the other two roots are 1 and 3.

Explanation

Explanation

ERUDITE ماہر ,  عالم

Explanation

• The set of complex numbers {1, i, -i, -1} under multiplication operation is a cyclic group.
• Two generators i and -i will covers all the elements of this group.
• Hence, it is a cyclic group.

Explanation

• 997 is a prime number, while 996, 998, and 999 are not.
  • 996 is divisible by 2, 3, 6, 12, ..., and is therefore not prime.
  • 998 is divisible by 2, 7, 14, ..., and is therefore not prime.
  • 999 is divisible by 3, 9, 27, ..., and is therefore not prime.

• So, the greatest 3-digit prime is 997.

Explanation

I hope everyone has learned something from this.​

Explanation:

• To use the correct verb form, we should always follow the rules of subject-verb agreement.
• Subject-verb agreement decides whether a subject is singular or plural.
• If the subject is considered to be singular then it will take singular verb.
• If the subject is considered to be plural, then it will take plural verb.
• According to the rules of subject-verb agreement, Indefinite pronouns are singular and they always take singular verb.

Explanation

• The correct answer is: y = vx, dy = vdx + xdv
• This substitution is used to solve homogeneous differential equations, as it allows for the separation of variables.
• By substituting y = vx and dy = vdx + xdv, the original equation can be transformed into a separable equation, which can then be solved by integrating both sides separately.

Explanation

• The correct answer is 7 and 11, as both values appear with the same frequency (three times).
• This is an example of a bimodal distribution, where there are two modes.

Explanation

L'Hospital's Rule is a technique used to evaluate limits of indeterminate forms, such as 0/0 or ∞/∞. The rule states that if the limit of the ratio of the derivatives of the numerator and denominator exists, then the original limit exists and is equal to that ratio.

The conditions for L'Hospital's Rule to work are:

• The function must be indeterminate, meaning it has the form 0/0 or ∞/∞.
• The derivative of the numerator and denominator must exist.
• The derivative of the denominator must be non-zero at the point being evaluated.