91Ó°ÊÓ

Which of the following functions is continuous at \(x=0 ?\) (A) \(f(x)\left\\{\begin{array}{ll}=\sin \frac{1}{x} & \text { for } x \neq 0 \\\ =0 & \text { for } x=0\end{array}\right.\) (B) \(f(x)\left\\{\begin{array}{ll}=\frac{x}{x} & \text { for } x \neq 0 \\ =0 & \text { for } x=0\end{array}\right.\) (C) \(f(x)\left\\{\begin{array}{ll}=x \sin \frac{1}{x} & \text { for } x \neq 0 \\\ =0 & \text { for } x=0\end{array}\right.\) (D) \(f(x)=\frac{x+1}{x}\)

Which of the following statements about the graph of \(y=\frac{x^{2}+1}{x^{2}-1}\) is not true? (A) The graph is symmetric to the \(y\) -axis. (B) There is no \(y\) -intercept. (C) The graph has one horizontal asymptote. (D) There is no \(x\) -intercept.

The \(x\) -coordinate of the point on the curve \(y=x^{2}-2 x+3\) at which the tangent is perpendicular to the line \(x\) \(+3 y+3=0\) is (A) \(-\frac{5}{2}\) (B) \(-\frac{1}{2}\) (C) \(\frac{7}{6}\) (D) \(\frac{5}{2}\)

\(\lim _{x \rightarrow 1} \frac{\frac{3}{x}-3}{x-1}\) is (A) -3 (B) -1 (C) 1 (D) 3

For polynomial function \(p, p^{\prime \prime}(2)=-6, p^{\prime \prime}(4)=0,\) and \(p^{\prime \prime}(5)=3 .\) Which must be true? (A) \(p\) has an inflection point at \(x=4\). (B) \(p\) has a minimum at \(x=4\). (C) \(p\) has a root at \(x=4\). (D) \((\mathrm{A})-(\mathrm{C})\) are all false.

\(\int_{0}^{6}|x-4| d x=\) (A) 6 (B) 8 (C) 10 (D) 12

\(\lim _{x \rightarrow \infty} \frac{3+x-2 x^{2}}{4 x^{2}+9}\) is (A) \(-\frac{1}{2}\) (B) \(\frac{1}{2}\) (C) 1 (D) nonexistent

The maximum value of the function \(f(x)=x^{4}-4 x^{3}+6\) on [1,4] is (A) 1 (B) 0 (C) 3 (D) 6

Let \(f(x)=\left\\{\begin{array}{ll}\frac{\sqrt{x+4}-3}{x-5} & \text { for } x \neq 5 \\ c & \text { for } x=5\end{array},\right.\) and let \(f\) be continuous at \(x=5 .\) Then \(c=\) (A) 0 (B) \(\frac{1}{6}\) (C) 1 (D) 6

\(\int_{0}^{\pi / 2} \cos ^{2} x \sin x d x=\) (A) -1 (B) \(-\frac{1}{3}\) (C) \(\frac{1}{3}\) (D) 1