题目
题目
单项选择题

Consider the function 𝑔 ( 𝑥 ) = 1 𝑥  on the interval [ − 1 , 1 ] . We know that 𝑔 ( − 1 ) = − 1 and 𝑔 ( 1 ) = 1 . Which of the following statements is correct?

选项
A.By the Squeeze Theorem we know there exists a number 𝑐 in the interval ( − 1 , 1 ) such that 𝑔 ( 𝑐 ) = 0 .
B.By the Intermediate Value Theorem we know there exists a number 𝑐 in the interval ( − 1 , 1 ) such that 𝑔 ( 𝑐 ) = 0 .
C.The Squeeze Theorem does not apply to this function on this interval.
D.By the Intermediate Value Theorem we know that 𝑔 ( 0 ) = 0 .
E.By the Squeeze Theorem we know lim 𝑥 ⟶ 0 𝑔 ( 𝑥 ) = 0 .
F.The Intermediate Value Theorem does not apply to this function on this interval.
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思路分析
We are given g(x) = 1/x on the interval [-1, 1], with g(-1) = -1 and g(1) = 1, and asked which statement is correct. Option 1: 'By the Squeeze Theorem we know there exists a number c in (-1, 1) such that g(c) = 0.' This is false because 1/x never equals zero for any x ≠ 0, so the equation g(c) = 0 has no solution. Moreover, the Squeeze Theorem is not the tool here since we do not have a pair of bounding functions that force g to be zero at some point. Option 2: 'By the Intermediate Value Theorem we know there exists a number c in (-1, 1) s......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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