Exceed can refer to going over or beyond a quantifiable or acceptable limit (exceed the speed limit; exceed their ability) or, more positively, to doing better than was anticipated (exceed our expectations). The range of this last sense extends to going beyond the outermost limits of something—or what seemed the outermost (a technology that will exceed the limits of brain imaging as we know it), and here it overlaps with the meaning of transcend. To transcend suggests both going beyond and rising entirely above the limits of something. A great speech that transcends the occasion it was written for, will have more than historical interest in the future because its truths have a broader reach. Frequent objects of transcend include boundaries, race, politics, division.
Both words describe people and things that affect us with their powerfully impressive or imposing presence that is of the highest dignity and grandeur. Majestic can refer to size, scope, or beauty, and suggests an exalted dignity (a majestic cathedral), but it is the natural world that most frequently inspires writers’ use of this word: majestic mountains; a majestic view; majestic creatures. August, the less common word, is most often applied to institutions, their members, and the associated architectural structures (the august halls of the U.S. Supreme Court). An august institution, body, assembly, or publication, inspires respect or reverence for its lofty purpose and the distinction and eminence of its members.
Both verbs refer to the doing or carrying out of something criminal, immoral, or otherwise wrong. Commit is the familiar verb we use with crime, specific crimes (commit murder), as well as with sins and errors. Perpetrate is a strong, but much less common, synonym for commit. It is most frequently applied to criminal acts, but takes a slightly wider range of objects. For example, it is common usage to say perpetrated a hoax, a scam, fraud, or violence, while commit would be used with fraud and violence, but normally not the first two. Perpetrate is used particularly for acts of deception, as in perpetrate a falsehood or perpetrate a myth. This may be because perpetrate can mean not only “carry out or execute,” but also “carry on.” Deceptions, such as hoaxes, scams, and myths can be carried on with, perpetuated, in ways a theft or murder can’t. It has been widely remarked, however, that writers may sometimes simply be confusing perpetrate and perpetuate.