3.)For the function g whose graph is given, state the value of each quantity, if

Question

3.)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.)

(a)    

lim t 0g(t)

(b)    

lim t 0+g(t)

(c)    

lim t 0 g(t)

(d)    

lim t 2g(t)

(e)    

lim t 2+g(t)

(f)    

lim t 2 g(t)

(g)    

g(2)

(h)    

lim t 4 g(t)

4.)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.

Find

lim t 12f(t)

and

lim t 12+f(t).

lim t 12f(t) =  mg

lim t 12+f(t) =  mg

7.)

(a) By graphing the function f(x) = (cos(2x) cos(x))/x2 and zooming in toward the point where the graph crosses the y-axis, estimate the value of lim x 0 f(x). (A graphing calculator is recommended.)

(b) Check your answer in part (a) by evaluating

f(x)

for values of x that approach 0. (Round your answers to six decimal places.)

f(0.1) = f(0.01) = f(0.001) = f(0.0001) = f(0.1) = f(0.01) = f(0.001) = f(0.0001) = lim x0 f(x) =

Explanation / Answer

Solution:

(a)    

lim t 0 g(t)

= -1

since graph is approaching toward y = -1 at x = 0-1


(b)    

lim t 0+ g(t)

= -2

approaching toward -2 at x = 0+

(c)    

lim t 0 g(t)

= Does Not Exist ( Left hand limit and right hand limit are not equal)

(d)    

lim t 2 g(t)

= 2


(e)    

lim t 2+ g(t)

= 0


(f)    

lim t 2 g(t)

= does not exist


(g)    

g(2) = 1 ( there dot just x = 2 )

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