Explanation

Explanation

Exonerated means cleared from blame or charges.

Sentence: "He was exonerated from all charges leveled against him." is grammatically and contextually correct.

Explanation

Given f(x) = x³ - (1/x³):

f(1/x) = (1/x)³ - (1/(1/x)³) = (1/x³) - x³

Now, let's calculate f(x) + f(1/x):

f(x) + f(1/x) = (x³ - 1/x³) + (1/x³ - x³)

= x³ - x³ - 1/x³ + 1/x³

= 0

Explanation

Most questions in English use an auxiliary verb like do, does, did, is, are, will, etc.

Example: "Do you like tea?" — "Do" is the auxiliary verb used to form the question.

Explanation

Coerced means forced or pressured to do something against one’s will.

Sentence: "He was coerced to give this confessional statement." makes logical and grammatical sense.

Explanation

In a sentence, the main verb and the direct object usually come together without any formal separator.

Example: "She reads books." — "reads" (main verb) is directly followed by "books" (direct object).

Explanation

The set {x: x ∈ N, x ≤ 10} has 10 elements (1, 2, 3, 4, 5, 6, 7, 8, 9, 10).

The cardinality of the power set of a set with n elements is 2^n.

So, the cardinality of the power set is 2^10 = 1024.

Explanation

1. Leibniz’s theorem gives a formula to find the nth derivative of the product of two functions.

2. It uses the binomial expansion:

Explanation

A preposition is typically followed by a noun or pronoun to complete its meaning.

Example: "She sat on the chair." — "on" (preposition) is followed by "the chair" (noun).

Explanation

"Exorbitantly" means excessively or unreasonably high, which fits well in the sentence:

"Fares are exorbitantly high in this city."