题目
题目

MAT135H5_F25_ALL SECTIONS 2.4 Preparation Check

多项选择题

Which of the following statements are TRUE? (Select all that apply.)  

选项
A.All trigonometric functions are continuous at every point in their domain
B.All polynomials are continuous at every point in  𝑅 .
C.All rational functions are continuous at every point in their domain
D.The function 𝑓 ( 𝑥 ) = 5 𝑥 + 4 𝑥 2 − 3 is a rational function, and it is continuous at every point in 𝑅 .
E.All piecewise defined functions are continuous at every point in their domain
F.All polynomials are continuous at every point in their domain
查看解析

查看解析

标准答案
Please login to view
思路分析
To evaluate which statements are TRUE, I’ll examine each option on its own terms and connect them to fundamental concepts about continuity. Option 1: 'All trigonometric functions are continuous at every point in their domain.' Trigonometric functions like sin, cos, and tan are continuous wherever they are defined. Since their domains are all real numbers for sin and cos, and for tan it’s all real numbers except the points where the denominator cos(x) is zero, this statement is true because we are considering continuity ......Login to view full explanation

登录即可查看完整答案

我们收录了全球超50000道考试原题与详细解析,现在登录,立即获得答案。

类似问题

Find the intervals on which the function is continuous. y =

For f(x) given below, find the numbers at which f is discontinuous. At which of these values is f continuous from the right, from the left, or neither? f(x)={2x if x≤1 3−x if 1<x≤4 √ x if x>4  

Let [math: f(x)] be the function that is equal to 0 for all rational [math: x] and 1 for every irrational [math: x]. Is [math: f(x)] continuous at [math: x=π]x=\pi?

What’s special about Thomae’s function? That one here:[math: t(x)={1 if x=0;1n if x is a rational number, x=m/n in lowest terms, n>0;0 if x is irrational.]t(x)= \begin{cases} 1 \quad &\text{ if $x=0$;} \\ \frac{1}{n} \quad &\text{ if $x$ is a rational number, $x=m/n$ in lowest terms, $n>0$;} \\ 0 \quad & \text{ if $x$ is irrational.} \end{cases}

更多留学生实用工具

加入我们，立即解锁 海量真题 与 独家解析，让复习快人一步！