Determine f’s end behavior f(x)= -5x^6+8x^5-1/ x^2 -9
1 answer:
Answer:
f(x) → -∞ as x → -∞
f(x) → -∞ as x → +∞
Step-by-step explanation:
The given function is;
f(x) = -5x^(6) + 8x^(5) - 1/(x² - 9x)
Using long division to divide this as attached, we have;
f(x) = -5x⁴ - 37x³ - 333x² - 2997x - 26973 + (-242757x - 1)/(x² - 9x)
Thus, the leading coefficient here is -5 and the polynomial degree is 4.
Since the leading coefficient is negative and the degree of the polynomial is an even number, then we can say that the behavior of the polynomial is;
f(x) → -∞ as x → -∞
f(x) → -∞ as x → +∞
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Answer:
d) The limit does not exist
General Formulas and Concepts:
<u>Calculus</u>
Limits
- Right-Side Limit:
- Left-Side Limit:
Limit Rule [Variable Direct Substitution]:
Limit Property [Addition/Subtraction]:
Step-by-step explanation:
*Note:
In order for a limit to exist, the right-side and left-side limits must equal each other.
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Find Right-Side Limit</u>
- Substitute in function [Limit]:
- Evaluate limit [Limit Rule - Variable Direct Substitution]:
<u>Step 3: Find Left-Side Limit</u>
- Substitute in function [Limit]:
- Evaluate limit [Limit Rule - Variable Direct Substitution]:
∴ Since , then
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits