91Ó°ÊÓ

Explain what is wrong with the statement. For the function \(f(x)=\sin (B x)\) with \(B>0,\) increasing the value of \(B\) increases the period.

Explain what is wrong with the statement. The equation \(y=2 x+1\) indicates that \(y\) is directly proportional to \(x\) with a constant of proportionality 2

Give an example of: A function with a vertical asymptote at \(x=3\) and \(\mathrm{de}\) fined only for \(x>3.\)

Explain what is wrong with the statement. The function \(y=\sin x \cos x\) is periodic with period \(2 \pi\)

Are the statements true or false? Explain. $$\begin{aligned} &\text { If } 0 \leq f(x) \leq a(x) \text { and } \lim _{x \rightarrow 0} a(x)=0, \text { then } \lim _{x \rightarrow 0} f(x)=\\\ &0 \end{aligned}$$

In Problems \(74-79,\) explain what is wrong with the statement. $$x^{5} > x^{3} \text { for } x > 0$$

Is the statement true or false? Assume that \(\lim _{x \rightarrow 7^{+}} f(x)=2\) and \(\lim _{x \rightarrow 7^{-}} f(x)=-2 .\) Explain. The function \((f(x))^{2}\) is continuous at \(x=7\).

Give an example of: A linear function with a positive slope and a negative \(x\) -intercept.

Are the statements true or false? Explain. $$\begin{aligned} &\text { If } b(x) \leq f(x) \leq a(x) \text { and } \lim _{x \rightarrow 0} b(x)=\lim _{x \rightarrow 0} f(x) \text { then }\\\ &\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} a(x) \end{aligned}$$

Is the statement true or false? Assume that \(\lim _{x \rightarrow 7^{+}} f(x)=2\) and \(\lim _{x \rightarrow 7^{-}} f(x)=-2 .\) Explain. If \(f(7)=2,\) the function \(f(x)\) is continuous at \(x=7\)