Which Situation is a good time to use a sentence fragment

What type of writing is demonstrated in this excerpt by general philip henry sheridan? at once i set about preparing for the examination which precedes admission to the military academy, studying zealously under the direction of mr. william clark; my old teachers, mcnanly and thorn, having disappeared from somerset and sought new fields of usefulness. the intervening months passed rapidly away, and i fear that i did not make much progress, yet i thought i should be able to pass the preliminary examination. that which was to follow worried me more and gave me many sleepless nights; but these would have been less in number, i fully believe, had it not been for one specification of my, outfit which the circular that accompanied my appointment demanded. this requirement was a pair of "monroe shoes." now, out in ohio, what "monroe shoes" were was a mystery—not a shoemaker in my section having so much as an inkling of the construction of the perplexing things, until finally my eldest brother brought an idea of them from baltimore, when it was found that they were a familiar pattern under another name. a. research essay b. persuasive essay c. biography d. memoir