Question

In: Math

1. f(x)= 3x / x^2 + 1 - Vertical Asymtote As x → −, f(x) →...

1.

f(x)= 3x / x^2 + 1

- Vertical Asymtote

As x, f(x) →

As x →  +, f(x) →

- Any hole in graph

- Horizontal asymtote

As x, f(x) →

As x →  +, f(x) →

Solutions

Expert Solution

The function f(x) is

---

Vertical Asymptotes is the values of x where the function becomes infinity and minus infinity which are points where the denominator becomes 0

This implies, there are NO Vertical Asymptotes

---

Holes are values of x where the function becomes indeterminate form 0/0.

This implies, there are NO HOLES

---

Horizontal asymptotes are values of y as x approaches infinity or minus infinity

Therefore, y=0 are horizontal asymptotes


Related Solutions

find f'(x) 1. f(x)=3sinx-secx+5 _______ 2. f(x)=e^xcot(3x) _______ 3. f(x)= cos^5(3x-1) _______
find f'(x) 1. f(x)=3sinx-secx+5 _______ 2. f(x)=e^xcot(3x) _______ 3. f(x)= cos^5(3x-1) _______
Consider f(x) = 2 + 3x^2 − x^3
Consider f(x) = 2 + 3x2 − x3 a) Find local max and min values b) Find intervals of concavity and infection points
Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and...
Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and f(1) = 1.
Find the Taylor series for f (x) = 2/(1+3x) at x = a where a =...
Find the Taylor series for f (x) = 2/(1+3x) at x = a where a = 0
Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals...
Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals where f is positive and where f is negative. Does f have any horizontal or vertical asymptotes. If so, find them, and show your supporting calculations. If not, briefly explain why not. Compute f′ and use it to determine the intervals where f is increasing and the intervals where f is decreasing. Find the coordinates of the local extrema of f Make a rough...
How do you find the domain of: f(g)= 5x^2+4 f(g)= 3x; -2<x<6 f(g)= (1) / 3x-6...
How do you find the domain of: f(g)= 5x^2+4 f(g)= 3x; -2<x<6 f(g)= (1) / 3x-6 f(g)= (x+2) / x^2-1 f(g)= x^4 / x^2+x-6 f(g)= sqrt (x+1) f(g)= sqrt (x^2+9)
compute the 2-degree polynomial approximation of f(x)= 3x-e^x^2
compute the 2-degree polynomial approximation of f(x)= 3x-e^x^2
consider the function f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and f''(x)=-10x^2-9x+5/(x^2+1)^5/2 a) find the local maximum and minimum...
consider the function f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and f''(x)=-10x^2-9x+5/(x^2+1)^5/2 a) find the local maximum and minimum values. Justify your answer using the first or second derivative test . round your answers to the nearest tenth as needed. b)find the intervals of concavity and any inflection points of f. Round to the nearest tenth as needed. c)graph f(x) and label each important part (domain, x- and y- intercepts, VA/HA, CN, Increasing/decreasing, local min/max values, intervals of concavity/ inflection points of f?
Find the derivatives of each of the following functions: 1. f(x) = (3x^2 + 2x −...
Find the derivatives of each of the following functions: 1. f(x) = (3x^2 + 2x − 7)^5 (2x + 1)^8 2. g(t) = cos(e^2x2+8x−3) 3. h(x) = e^x2/tan(2x−3) 4. Find dy/dx if cos(xy) = x^2y^5
consider the function f(x) = 1 + x3  e-.3x a. what is f'(x) b. what is f''(x)...
consider the function f(x) = 1 + x3  e-.3x a. what is f'(x) b. what is f''(x) c. what are the critical points of f(x) d. are the critical points a local min or local max or neither? e. find the inflection points f. if we define f(x) to have the domain of [2,50] compute the global extreme of f(x) on that interval
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT