# Calculus

## In these exercises, make reasonable assumptions about the graph of the indicated function outside of the region depicted. For the function g graphed in the accompanying figure, find lim x right 0- g(x) lim x rightarrow 0+ g(x) lim x rightarrow 0 g(x) g(0).

EXPERT ANSWER a) When x = 0, we are talkin about the y-axis And when they ask us to find the limit as x —> 0(-), we are looking at the value of y when x is approaching 0 from the negative side. Notice that at x = 0, y = 3. Also, when x …

## Sketch the graph of the function.

Sketch the graph of the function. f(x) = 4 + x if x < −2 x2 if −2 ≤ x < 2 6 − x if x ≥ 2 Use the graph to determine the values of a for which lim x → a f(x) does not exist. (Enter your answers as a comma-separated list.) a = EXPERT ANSWER

## Sketch the graph of the function.

Sketch the graph of the function. f(x) = 4 + x if x < ?1 x2 if ?1 ? x < 1 2 ? x if x ? 1 Use the graph to determine the values of a for which lim x ? a f(x) does not exist. (Enter your answers as a comma-separated list.) a = EXPERT ANSWER

## 2.)Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)

2.)Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) (a) lim x → 2− f(x) (b) lim x → 2+ f(x) (c) lim x → 2 f(x) (d) f(2) (e) lim x → 4 f(x) (f) f(4) EXPERT ANSWER

## For the function f whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)

For the function f whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) (a) lim x?1 f(x) (b) lim x?3? f(x) (c) lim x?3+ f(x) (d) lim x?3 f(x) (e) f(3) EXPERT ANSWER

## Sketch the graph of the function.

Sketch the graph of the function. f(x) = 3 + x if x < −2 x2 if −2 ≤ x < 2 6 − x if x ≥ 2 *The lower left hand graph is the correct graph!Use the graph to determine the values of a for which lim x → a f(x) does not exist. (Enter your answers as a comma-separated list.) a = EXPERT ANSWER

## Sketch the graph of an example of a function f that satisfies all of the given conditions. lim x → 0− f(x) = 2, lim x → 0+ f(x) = −1, f(0) = 1

Sketch the graph of an example of a function f that satisfies all of the given conditions. lim x → 0− f(x) = 2, lim x → 0+ f(x) = −1, f(0) = 1 EXPERT ANSWER

## For the function h whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)

For the function h whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) EXPERT ANSWER (a)     lim x → −3− h(x)= (b)     lim x → −3+ h(x)= (c)     lim x → −3 h(x)= (d)     h(−3)= (e)     lim x → 0− h(x)= (f)     lim x → 0+ h(x)= (g)     lim x → 0 h(x)= (h)     h(0)= (i)     lim x → 2 h(x)= (j)     h(2)= (k)     lim x → 5+ h(x)= (l)     lim x → 5− h(x)= EXPERT ANSWER a) 4b)4c)4d)DNEe)1f)-1g)DNEh)1i)2j)DNEk)3 l)from the …

## For the function R whose graph is shown, state the following. (If an answer does not exist, enter DNE.)

For the function R whose graph is shown, state the following. (If an answer does not exist, enter DNE.) (a) lim x ? 2 R(x) (b) lim x ? 5 R(x) (c) lim x ? ?3? R(x) (d) lim x ? ?3+ R(x) (e) The equations of the vertical asymptotes. x = (smallest value) x = x = (largest value) EXPERT ANSWER a) At x = 2, both sides …