Properties of Limits

Practice 1:

(a) -10

(b) 24

(c) 3/2

(d) 0

(e) 0

(f) 5/4

(g) -64

(h) 2

Practice 2:

(a) 39

(b) -3/5

(c) 2/3

Practice 3:

(a) 0

(b) 2

(c) 3

(d) 1

Practice 4:

(a) slope of the line tangent to the graph of $\mathrm{g}$ at the point $(1, \mathrm{~g}(1)):$ estimated slope $\approx-2$

(b) slope of the line tangent to the graph of $\mathrm{g}$ at the point $(3, \mathrm{~g}(3)):$ estimated slope $\approx 0$

(c) slope of the line tangent to the graph of $\mathrm{g}$ at the point $(0, \mathrm{~g}(0)):$ estimated slope $\approx 1$

Practice 5: $\quad \lim\limits_{x \rightarrow 1} x^{2}+2=3$ and $\lim\limits_{x \rightarrow 1} 2 x+1=3$ so $\lim\limits_{x \rightarrow 1} f(x)=3$.

Practice 6: $\lim\limits_{x \rightarrow 0} \cos (\mathrm{x})=1$ and $\lim\limits_{x \rightarrow 0} 1=1$ so $\lim\limits_{x \rightarrow} \frac{\sin (x)}{x}=1.$