# Calculus

## 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 …

## A patient receives a 150-mg injection of a drug every 4 hours. The graph shows the amount f(t) of the drug in the bloodstream after t hours.

EXPERT ANSWER lim t –> 4- = 75lim t –> 4+ = 225 The – indicates the t-value is approaching 4 from numbers lower than 4. At t = 0 the patient gets the first injection and there is 150 mg in the blood. Over time this amount decreases as shown by the curve. At …

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

For the function f whose graph is shown, state the following. (If an answer does not exist, enter DNE.) (e) lim x → 6+ f(x) (f) The equations of the vertical asymptotes. x = ____ (smallest value) x = x = x = ____ (largest value) EXPERT ANSWER

## For the function g whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) lim g(t) t ? 0?

EXPERT ANSWER a) lim t -> 0- g(t) =-1 b) lim t -> 0+g(t) =-2 c)lim t ->0 g(t) =DNE d)lim t ->2- g(t) = 2 e) lim t ->2+ g(t) = 0 f) lim t ->2 g(t) = DNE g) g(2) = 1 h) lim t ->4 g(t) = 3

## solve for x if 2x^2 − 4x + 1 = 0

solve for x if 2x^2 − 4x + 1 = 0 EXPERT ANSWER