If f(t) = 2t – t^2 , what is (f(t+h) – f(t))/h ?
回答 (1)
2015-09-09 4:44 pm
= ((2(t + h) - (t + h)^2) - (2t - t^2)) / h
= (((2t + 2h) - (t^2 + 2th + h^2)) - (2t - t^2)) / h
= ((2t + 2h - t^2 - 2th - h^2) - (2t - t^2)) / h
= (2t + 2h - t^2 - 2th - h^2 - 2t + t^2) / h
= (2h - 2th - h^2) / h
= 2 - 2t - h
NOTE: If h approaches zero, we have 2 - 2t, which is f'(t)
= (((2t + 2h) - (t^2 + 2th + h^2)) - (2t - t^2)) / h
= ((2t + 2h - t^2 - 2th - h^2) - (2t - t^2)) / h
= (2t + 2h - t^2 - 2th - h^2 - 2t + t^2) / h
= (2h - 2th - h^2) / h
= 2 - 2t - h
NOTE: If h approaches zero, we have 2 - 2t, which is f'(t)
收錄日期: 2021-05-01 15:22:00
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150909083630AAhKgOF