F(x)=(2x-1)/abs(x)
Find:
A) lim as x approaches infinity of f(x)
B) lim as x approaches negative infinity of f(x)
C) lim as x approaches 0 from the right of f(x)
D) lim as x approaches 0 from the left of f(x)
E) all horizontal asymptotes
F) all vertical asymptotes

Question

F(x)=(2x-1)/abs(x) 
Find:
A) lim as x approaches infinity of f(x)
B) lim as x approaches negative infinity of f(x) 
C) lim as x approaches 0 from the right of f(x)
D) lim as x approaches 0 from the left of f(x)
E) all horizontal asymptotes 
F) all vertical asymptotes

debbieg · Answer

For (A) - (D), just re-write the function without abs value, keeping in mind what is happening with x.

E.g., as x->infinity, |x|=x (since x is positive)

As x->-infinity, |x|=-x (since x is negative)

Find each limit, using the version of the function written without abs value.

After you have A, B, C, and D, the vertical and horizontal asymptotes should be clear. (That is really what you are finding in A-D.)