There are frogs and koi in a pond, and the number of frogs and the number of koi in the pond are independent. Let X represent th
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Answer: x ≈ 1.59688927, −1.60312387, −4.67045686, 4.69039614, 7.872914, −7.91513776, −10.89002194
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Simplify 2*cosx*(2x+30°) + √3=0
Simplify each term.
Apply the distributive property.
- 2 cos ( x ) ( 2 x ) + 2 cos ( x ) * 30 ° + √ 3 = 0
- Multiply 2 by 2
- 4 cos ( x ) x + 2 cos ( x ) *30 ° + √ 3 = 0
- Multiply 30 °by 2
- 4 cos ( x ) x + 60 cos ( x ) + √ 3 = 0
- Reorder factors in 4 cos ( x ) x + 60 cos ( x ) + √3
- 4xcos(x)+60cos(x)+√3=0
- Graph each side of the equation. The solution is the x-value of the point of intersection. x ≈ 1.59688927 , − 1.60312387 , − 4.67045686 , 4.69039614 , 7.872914 , − 7.91513776 , − 10.89002194
a) Since both limits are <em>distinct</em> and do not exist, we conclude that x = - 1 is not part of the domain of the <em>rational</em> function.
b) The function is equivalent to the function
.
<h3>How to determine whether a limit exists or not</h3>
According to theory of limits, a function f(x) exists for x = a if and only if . This criterion is commonly used to prove continuity of functions.
<em>Rational</em> functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following <em>lateral</em> limits:
Since both limits are <em>distinct</em> and do not exist, we conclude that x = - 1 is not part of the domain of the <em>rational</em> function.
In addition, we can simplify the function by <em>algebra</em> properties:
The function is equivalent to the function
.
To learn more on lateral limits: brainly.com/question/21783151
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