# Infinite Limits and Vertical Asymptotes

In mathematics, the concept of infinite limits and vertical asymptotes plays a crucial role in understanding the behavior of functions as they approach certain points. Infinite limits occur when a function approaches positive or negative infinity as the input approaches a particular value. Vertical asymptotes are vertical lines that a function approaches but never crosses, often occurring when the function's value becomes unbounded as the input approaches a certain value. Together, these phenomena offer insights into the behavior of functions at critical points, shedding light on their overall structure and behavior.

Questions

- How do you determine the limit of #5^x/(3^x+2^x)# as x approaches infinity?
- For what values of x, if any, does #f(x) = x/(xe^x-3) # have vertical asymptotes?
- For what values of x, if any, does #f(x) = 1/((2x+3)(x-6) # have vertical asymptotes?
- How do you find the limit of #x / sqrt (4x^2 + 2x +1) # as x approaches infinity?
- For what values of x, if any, does #f(x) = 1/((x+2)(x-1)) # have vertical asymptotes?
- For what values of x, if any, does #f(x) = 1/((x-2)(x-1)(e^x-3)) # have vertical asymptotes?
- What is the vertical asymptote of #y=1/x#?
- How do you find vertical asymptotes in calculus?
- For what values of x, if any, does #f(x) = 1/((x+3)(x-2)) # have vertical asymptotes?
- For what values of x, if any, does #f(x) = 1/((x-2)(x-2)(e^x-3)) # have vertical asymptotes?
- How do you find the limit of #e^(-3x)# as x approaches infinity?
- For what values of x, if any, does #f(x) = 1/((x+12)(x^2-36)) # have vertical asymptotes?
- How do you find the limit of #sqrt(x^2 + 1) - x# as x approaches infinity?
- For what values of x, if any, does #f(x) = 1/((x-5)sin(pi+1/x) # have vertical asymptotes?
- For what values of x, if any, does #f(x) = 1/((x+3)(x+9)) # have vertical asymptotes?
- For what values of x, if any, does #f(x) = 1/(x^2-4x+4) # have vertical asymptotes?
- How do you find the limit of # (2^x-3^-x)/(2^x+3^-x)# as x approaches infinity?
- What is the vertical asymptote of ln(x)?
- For what values of x, if any, does #f(x) = sec((-15pi)/8+9x) # have vertical asymptotes?
- What is #lim t->-∞# of #(t^2+2)/(t^3+t^2-1)#?