Asymptotes for arctan(x)-1/(x-1)

Question

Need help getting horizontal and vertical asymptotes for that function

Answer 1

Hi Raj u need to follow regular steps to find vertical Asmpt. and horizontal Asmpt.

 

1-  F(x) = x - 1/(x-1) combine the denominator (x^2 - x -1)/ (x-1)  

 

2- to find Vertical Asmpt   make the denominator equal to zero, x -1 =0 , add one to both side,

    so x=1 this is vertical Asmpt. because when x=1 the function will be (x^2 - x - 1)/ 0 ,  undefined ( simply when F(x) = ∞).

 

3- to find Horizontal Asmpt which simply is x approaching ∞. to do that 1st find highest degree of numerator 2nd           divide the both the numerator and denominator from that degree

 

 

    x^2 is highest degree in numerator  x^2 ÷ (x^2 - x -1) / (x^2 ÷ ( x-1)) so the function will be

 

   (1 - 1/X - 1/x^2) / (1/X - 1/x^2) after cross out x^2 from both the numerator and denominator 

 

   now if we let x = ∞, and we know that any number divided by ∞ equals zero. the function will looks like

 

 

   F(x) = (1 - 1/∞ - 1/∞) / (1/∞ - 1/∞) then F(x) =1 is the horizontal Asmpt 

 

Hopefully this answers your question 

Good Luck