find the equation of the vertical asymptote(s) of the function f(x)=x^5/(x - 2)^2 :\no f(x) has no vertical…

find the equation of the vertical asymptote(s) of the function f(x)=x^5/(x - 2)^2 :\no f(x) has no vertical asymptotes\no x = 2\no x = 0\no x = -2

find the equation of the vertical asymptote(s) of the function f(x)=x^5/(x - 2)^2 :\no f(x) has no vertical asymptotes\no x = 2\no x = 0\no x = -2

Answer

Explanation:

Step1: Recall vertical - asymptote condition

Vertical asymptotes occur where the denominator of a rational function is zero and the numerator is non - zero. For the function $f(x)=\frac{x^{5}}{(x - 2)^{2}}$, set the denominator equal to zero. $(x - 2)^{2}=0$

Step2: Solve the equation for x

Taking the square - root of both sides of $(x - 2)^{2}=0$, we get $x-2 = 0$. Solving for $x$, we have $x = 2$. When $x = 2$, the numerator $x^{5}=2^{5}=32\neq0$.

Answer:

B. $x = 2$