(5)

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Step 1:

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The function is $\"\"$ on interval $\"\"$ .

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Intermediate value theorem:

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If $\"\"$ is continuous on the closed interval $\"\"$ , $\"\"$ , and $\"\"$ is any number between $\"\"$ and $\"\"$ , then there is at least one number in $\"\"$ such that $\"\"$ .

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In this case $\"\"$ .

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Find $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Step 2:

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Find $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The function $\"\"$ is continuous on $\"\"$ with $\"\"$ and $\"\"$ .

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By intermediate value theorem, there must be some $\"\"$ in $\"\"$ such that $\"\"$ .

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The function $\"\"$ has a zero in the closed interval $\"\"$ .

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Solution:

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The function $\"\"$ has a zero in the closed interval $\"\"$ .

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(6)

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Step 1:

\

The function is $\"\"$ on interval $\"\"$ .

\

Intermediate value theorem:

\

If $\"\"$ is continuous on the closed interval $\"\"$ , $\"\"$ , and $\"\"$ is any number between $\"\"$ and $\"\"$ , then there is at least one number in $\"\"$ such that $\"\"$ .

\

In this case $\"\"$ .

\

Find $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Step 2:

\

Find $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The function $\"\"$ is continuous on $\"\"$ with $\"\"$ and $\"\"$ .

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By intermediate value theorem, there must be some $\"\"$ in $\"\"$ such that $\"\"$ .

\

The function $\"\"$ has a zero in the closed interval $\"\"$ .

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Solution:

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The function $\"\"$ has a zero in the closed interval $\"\"$ .

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$\"\"$ and $\"\"$

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