Question 1179792: Which combination of limit properties is required to evaluate this limit?
lim x-->4 (24/x-2x+2)^3
a. sum, difference, product, root
b. sum, difference, product, power
c. sum, difference, quotient, power
d. sum, difference, quotient, root
e. A limit does not exist.
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! To evaluate the limit:
lim (x→4) (24/x - 2x + 2)³
We need to break down the expression and apply the appropriate limit properties:
1. **Quotient:** We have a term 24/x, which requires the quotient rule for limits.
2. **Difference:** We have terms (24/x) - 2x, which requires the difference rule for limits.
3. **Sum:** We have terms (24/x - 2x) + 2, which requires the sum rule for limits.
4. **Power:** The entire expression is raised to the power of 3, which requires the power rule for limits.
Therefore, the combination of limit properties required is:
* Sum
* Difference
* Quotient
* Power
The correct answer is **c. sum, difference, quotient, power**.
Answer by ikleyn(52824)  (Show Source):
You can put this solution on YOUR website! .
Which combination of limit properties is required to evaluate this limit?
lim x-->4 (24/x-2x+2)^3
a. sum, difference, product, root
b. sum, difference, product, power
c. sum, difference, quotient, power
d. sum, difference, quotient, root
e. A limit does not exist.
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In order for to discuss this problem, we first need to read what is written there.
But i is not possible to read this function properly, since it is written incorrectly.
To write correctly, use parentheses to show clearly which part is the numerator
and which part is the denominator in the formula.
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