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3 years ago

Over what interval will the immediate value theorem apply

Mathematics

1 answer:

koban [17]3 years ago

6 0

Answer:

Any [a,b] that does NOT include the x-value 3 in it.

Either an [a,b] entirely to the left of 3, or

an [a,b] entirely to the right of 3

Step-by-step explanation:

The intermediate value theorem requires for the function for which the intermediate value is calculated, to be continuous in a closed interval [a,b]. Therefore, for the graph of the function shown in your problem, the intermediate value theorem will apply as long as the interval [a,b] does NOT contain "3", which is the x-value where the function shows a discontinuity.

Then any [a,b] entirely to the left of 3 (that is any [a,b] where b < 3; or on the other hand any [a,b] completely to the right of 3 (that is any [a,b} where a > 3, will be fine for the intermediate value theorem to apply.

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Firdavs [7]

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3 years ago

If sine theta almost-equals 0. 3090 , what is the approximate value of csc Theta? 0. 5559 1. 3090 3. 2362 10. 4733.

Sedaia [141]

Reciprocal of trigonometric ratios are also trigonometric ratios. The approximate value of csc(θ) for the corresponding given value of sin(θ) is given by: Option: C: 3.2362

<h3>What are the six trigonometric ratios?</h3>

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

$\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\$

Thus, we see that $\sin(\theta) = \dfrac{1}{\csc{\theta}}$ for a specific angle θ, we get:

Actually, reciprocal of each trigonometric ratio will be a trigonometric ratio, for specific angle.

For the considered case, we're given that,

$\sin(\theta) \approx 0.3090$

$\sin(\theta) = \dfrac{1}{\csc(\theta)}\\\\\csc(\theta) = \dfrac{1}{\sin(\theta)} \approx\dfrac{1}{0.3090} \approx 3.2362$

Thus, the approximate value of csc(θ) for the corresponding given value of sin(θ) is given by: Option: C: 3.2362

Learn more about trigonometric ratios here:

brainly.com/question/22599614

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Answer:

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How many distinct and real roots can an nth-degree polynomial have?

Vlad [161]

The fundamental theorem of algegra is often cited to say that an n-th degree polynomial has n roots. They may not always be distinct, and they may not always be real.

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3 years ago

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