多倫多大學(xué)的微積分課程學(xué)習(xí)眾多數(shù)學(xué)主題，不少同學(xué)總是覺得課程很難，考試也不知道怎么備考。下面我們提供一些這門課程經(jīng)常會(huì)出現(xiàn)的一些作業(yè)題目，同學(xué)們在平時(shí)學(xué)習(xí)中或者考前復(fù)習(xí)時(shí)都可以用這些題目來做提升訓(xùn)練。

一、課程內(nèi)容

unit1：邏輯、集合、符號(hào)、定義和證明

unit2：極限和連續(xù)性

unit3：導(dǎo)數(shù)

unit4：超越函數(shù)

unit5：中值定理及其應(yīng)用

unit6：極限和導(dǎo)數(shù)的應(yīng)用

unit7：積分的定義

unit8：微積分的基本定理

unit9：積分方法

unit10：積分的應(yīng)用

unit11：序列

unit12：反常積分

unit13：系列

unit14：冪級(jí)數(shù)和泰勒級(jí)數(shù)

二、作業(yè)題分享

1.Negate each of the following statements without using any negative words (‘no’,‘not’,‘none’,etc):

(a) “Every page in this book contains at least one word whose first and last letters both come alphabetically before M.”

(b) “I have a friend all of whose former boyfriends had at least two siblings with exactly three different vowels in their name.”

(c) “If a student in this class likes the musical Cats then they are not my friend.”

2. Consider the following definitions about real numbers x:

? x is courageous when ?a >0,x< a

? x is hard-working when ?a ≥ 0,x< a

? x is intelligent when ?a >0,x ≤ a

? x is ambitious when ?a ≥ 0,x ≤ a

3.Given a real number x,we defined the floor of x,denoted by b xc,as the largest integer smaller than or equal to x. For example,[π] = 3,[ 7 ] = 7,and [?0.5] = ?1.

(a) Sketch the graph of this function. At which points is the function f(x) = [x] continuous? Which discontinuities are removable and which ones are nonremovable?

(b) Consider the function h(x) = [sin x] . Show that h has exactly one removable and one non-removable discontinuity inside the interval (0,2π).

4.The functions G and H have both domain R. They are continuous everywhere. They satisfy G(0) = 0 and H(0) = 0. Moreover,G0 = g and H0 = h,where g and h are the functions in Question 2. Sketch the graphs of G and H.

5.You know what your final answers should be. Just make sure that at each point you are only using things that have already been proven.

6.Now we have a bar which lies on the x-axis,from the position x = 1 to the position x = 7 (all values of x are measured in meters). The bar is made of different materials. Between x = 1 and x = 2,the density of the bar is 2kg/m; between x = 2 and x = 5,the density is 3kg/m; between x = 5 and x = 5.5,the density is 10kg/m,and between x = 5.5 and x = 7,the density is 1kg/m. What is the total mass of the bar?

三、微積分課程作業(yè)基本解題思路

審題→繪圖→思考方法并選擇→套用定理or公式→邊界條件→檢查計(jì)算過程

1.審題時(shí)需要你明確這道題目的具體要求，找到關(guān)鍵信息，尤其是一些隱含條件。對(duì)于有些題目，需要繪圖才能更清晰地知道怎么解題。一道題目也可能不止一種解題方式，在解題時(shí)，你往往需要決定使用哪種方法，另外可以根據(jù)題目特點(diǎn)選擇恰當(dāng)?shù)奈⒎e分方法，比如求導(dǎo)、積分、極限等等。

解題過程中，一些基本定理和公式是關(guān)鍵，導(dǎo)數(shù)、積分、微分中值定理分別是什么，怎么使用，這些在你練題之前都可以先復(fù)習(xí)一遍。最后，做完題目，一定不能忘記檢查，不要犯一些低級(jí)錯(cuò)誤。

以上是多倫多大學(xué)的大一微積分課作業(yè)相關(guān)問題分享，希望可以幫助大家更了解題目出題方式。在學(xué)習(xí)過程中有任何問題，同學(xué)們都可以直接向留求藝的專業(yè)老師提問!