YouLet 2x^4 + 5x^3 + 3x^2 + 2x - 50 / x^4 + 3. What is the equation of the horizontal asymptote of f(x) and from what direction does f(x) approach the asymptote as x tends to positive infinity?
Question
YouLet 2x^4 + 5x^3 + 3x^2 + 2x - 50 / x^4 + 3. What is the equation of the horizontal asymptote of f(x) and from what direction does f(x) approach the asymptote as x tends to positive infinity?
Solution
The equation of the horizontal asymptote of the function f(x) = (2x^4 + 5x^3 + 3x^2 + 2x - 50) / (x^4 + 3) is y = 2. This is because the degree of the numerator and the denominator are the same (both are 4), so the horizontal asymptote is the ratio of the leading coefficients, which is 2/1 = 2.
As x tends to positive infinity, f(x) approaches the asymptote from below. This is because the leading term of the numerator (2x^4) is less than the leading term of the denominator (x^4) when x is positive. Therefore, as x increases, the value of f(x) gets closer and closer to 2 from below.
Similar Questions
The line y = 4 is a horizontal asymptote to the right of the graph of a function f. What is the limit of f as x approaches infinity?
Vertical asymptotes at x = 4) Horizontal asymptote at y
Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list of equations.)
Sketch the graph of a function that satisfies all of the given conditions.vertical asymptote x = 0,f ′(x) > 0 if x < −3,f ′(x) < 0 if x > −3 (x ≠ 0),f ″(x) < 0 if x < 0,f ″(x) > 0 if x > 0
Task 4.The following graph represents a rational function.(i) Identify the horizontal and vertical asymptotes (if any). Explain how you would find horizontal and vertical asymptotes of any rational function mathematically.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.