Home > Calculus > Infinite Limits and Vertical Asymptotes

For what values of x, if any, does #f(x) = -tan(pi/6-x) # have vertical asymptotes?

Answer 1

William Abdalla

#f(x)# have Vertical Asymptotes for #x=-pi/3+-n*180#

where #n=0, 1, 2, 3.....#

From the given #f(x)=-tan(pi/6-x)#

Set the angle #(pi/6-x)=pi/2# because #tan (pi/2)=#undefined

Solving for #x#

#x=-pi/3#

and for tangent function the values are the same everytime #pi# or multiples of #pi# are added or subtracted. Therefore, the function has asymptotes for values of #x=pi/3+-n*pi# where #n=0, 1, 2, 3,.....# Examples:

#x=-pi/3#

#x=-(4pi)/3#

#x=(2pi)/3#

#x=(5pi)/3#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Scarlett Allison

The function f(x) = -tan(pi/6-x) has vertical asymptotes at x = pi/6 + n*pi, where n is an integer.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.