the graph of the function f(x) = sec x is given above for the interval x ∈ 0,2π only. determine the one…

the graph of the function f(x) = sec x is given above for the interval x ∈ 0,2π only. determine the one - sided limit. then indicate the equation of the vertical asymptote. find lim x→(π/2)^+ f(x) = . this indicates the equation of a vertical asymptote is x = π/2. find lim x→(3π/2)^+ f(x) = . this indicates the equation of a vertical asymptote is x = 3π/2.

the graph of the function f(x) = sec x is given above for the interval x ∈ 0,2π only. determine the one - sided limit. then indicate the equation of the vertical asymptote. find lim x→(π/2)^+ f(x) = . this indicates the equation of a vertical asymptote is x = π/2. find lim x→(3π/2)^+ f(x) = . this indicates the equation of a vertical asymptote is x = 3π/2.

Answer

Answer:

  1. $\lim_{x\rightarrow(\frac{\pi}{2})^{+}}f(x)=-\infty$
  2. $\lim_{x\rightarrow(\frac{3\pi}{2})^{+}}f(x)=\infty$

Explanation:

Step1: Recall the definition of secant

$\sec x=\frac{1}{\cos x}$

Step2: Analyze $\lim_{x\rightarrow(\frac{\pi}{2})^{+}}$

As $x\rightarrow(\frac{\pi}{2})^{+}$, $\cos x\rightarrow0^{-}$. Then $\frac{1}{\cos x}\rightarrow-\infty$ since $\frac{1}{\text{small negative number}}\rightarrow-\infty$.

Step3: Analyze $\lim_{x\rightarrow(\frac{3\pi}{2})^{+}}$

As $x\rightarrow(\frac{3\pi}{2})^{+}$, $\cos x\rightarrow0^{+}$. Then $\frac{1}{\cos x}\rightarrow\infty$ since $\frac{1}{\text{small positive number}}\rightarrow\infty$.