Which combination of limit properties is required to evaluate this limit?
lim
x->((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.
x->4**
I chose C. Is that correct?
I guess, though product is also involved
lim(2x) = 2 * lim(x)
But I guess C is closest.
To evaluate the given limit, we need to consider the properties of limits. Let's break down the expression and identify the necessary limit properties:
The expression is a cubic function of ((24/x)-2x+2) raised to the power of 3.
To evaluate this limit, we need to apply the power property of limits, which states:
If the limit of f(x) as x approaches a exists, then the limit of [f(x)]^n as x approaches a is equal to the limit of f(x) as x approaches a raised to the power of n.
Therefore, the required limit property is the power property.
Looking at the answer choices:
A) sum, difference, product, root - The root property is not required.
B) sum, difference, product, power - The power property is needed.
C) sum, difference, quotient, power - The quotient property is not required.
D) sum, difference, quotient, root - The quotient property and root property are not required.
E) A limit does not exist - The given expression does not indicate that the limit does not exist.
Hence, the correct answer is B) sum, difference, product, power.