Difference between revisions of "Week4a"

Activity: interpreting limits from a graph.

Below is the graph of a function f:

Compute the following limits. Note that some of your answers will only be approximate.

a) $f(0)$

b) $f(1.5)$

c) $f(1)$

d) $f(0.9)$

e) $f(1.1)$

f) $\lim_{x\rightarrow 1^+} f(x)$

g) $\lim_{x\rightarrow 1^-} f(x)$

h) $\lim_{x\rightarrow 1} f(x)$

i) $f(1.9)$

j) $f(2.1)$

k) $\lim_{x\rightarrow 2} f(x)$

l) $f(f(1.9))$

m) $f(f(2.1))$

n) $\lim_{x\rightarrow 2^+} f(f(x))$

o) $\lim_{x\rightarrow 2^-} f(f(x))$

p) $\lim_{x\rightarrow 2} f(f(x))$

q) $\lim_{x\rightarrow -1} f(f(x))$

r) $\lim_{x\rightarrow 4} f(f(x))$

s) $\lim_{x\rightarrow -4} f(f(x))$

t) $\lim_{x\rightarrow 0} f(1+x^2)$

u) $\lim_{x\rightarrow 0} f(\cos{x})$

Question.

The statement, “Whether or not $\lim_{x\rightarrow a} f(x)$ exists depends on how $f(a)$ is defined,” is true

a) Never.

b) Sometimes.

c) Always.

Question.

If a function $f$ is not defined at $x=a$, then

a) $\lim_{x\rightarrow a} f(x)$ cannot exist.

b) $\lim_{x\rightarrow a} f(x)$ could be 2.

c) $\lim_{x\rightarrow a} f(x)$ must approach infinity.

d) Not enough information.