Practice Exam A Answer Key

$f(2)=7$, while the limit is $4$. The filled point gives the first; nearby graph behavior gives the second.

Defined value, existing two-sided limit, equality between them.

It records simultaneous numerator and denominator convergence to zero but does not determine their relative rates.

IVT guarantees at least one attained intermediate value under continuity; it does not calculate or prove uniqueness.

$-13$.

Factor and cancel to obtain $x+3$; answer $6$.

Rationalization gives $1/(\sqrt{x+9}+3)$; answer $1/6$.

Combine fractions to obtain $-1/(2x)$; at $2$, answer $-1/4$.

$(7/2)(\sin7x/7x)\to7/2$.

Squeezed between $-x^2$ and $x^2$; answer $0$.

Left $-1$, right $1$; answer $\mathrm{DNE}$.

Numerator approaches $3>0$; denominator changes sign. Left $-\infty$, right $+\infty$.

$5/2$.

$-1$.

Hole at $1$, vertical asymptote $x=2$, horizontal asymptote $y=1$.

$2k+1=3$, so $k=1$.

The polynomial is continuous; values at $1,2$ are $-1,7$, so a root exists.

$\delta=\varepsilon/2$.