题目
题目

MAT135H5_F25_ALL SECTIONS 2.4 Preparation Check

多重下拉选择题

We will discuss the Intermediate Value Theorem Links to an external site. in more detail during class. However, here is a warm-up question which will help you prepare for class: Which of the following statements are TRUE?  a) If 𝑓 ( 𝑥 ) is continuous on the interval [ 0 , 5 ] and 𝑓 ( 0 ) = 1 and 𝑓 ( 5 ) = 2 , then the Intermediate Value Theorem says that there is a number 𝑐 in [ 0 , 5 ] such that 𝑓 ( 𝑐 ) = 2 . [ Select ] False True   b) If 𝑓 ( 𝑥 ) is continuous on the interval [ 2 , 4 ]  and 𝑓 ( 2 ) < 0  and 𝑓 ( 4 ) > 0 , then the Intermediate Value Theorem says that 𝑓 ( 3 ) = 0 .  [ Select ] True False   c) If 𝑓 ( 𝑥 ) is any function and 𝑓 ( 𝑎 ) = 4  and 𝑓 ( 𝑏 ) = 6 , then the Intermediate Value Theorem says that there is a number 𝑐 in [ 𝑎 , 𝑏 ]  satisfying 𝑓 ( 𝑐 ) = 5 . [ Select ] True False

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思路分析
We begin by restating the warm-up question and the three statements to be evaluated, so we can inspect each one carefully before deciding which are true or false. Option a) If f(x) is continuous on the interval [0,5] and f(0)=1 and f(5)=2, then the Intermediate Value Theorem says that there is a number c in [0,5] such that f(c)=2. - Here, the given endpoint value f(5) already equals 2. Since c can be taken as 5 (which lies in the closed interval [0,5]), the statement that there exists a c with f(c)=2 on [0,5] is satisfied. The IVT guarantees that every intermediate value betwee......Login to view full explanation

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Let [math: f] be a continuous function defined on the domain [math: [0,2]][0,2]. If [math: f(0)=1] and [math: f(2)=3], then the equation [math: f(x)=0] has no solution.

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