Find the value it of the constant a that makes the following function continuous

Question

Find the value it of the constant a that makes the following function continuous on (-infinity,infinity). Find the value of the constant c that makes the following function continuous on (-infinity,infinity). Show that has a jump discontinuity at x 5 by calculating the limit as x approaches 5 from the left and from the right. Find the values of the constant b that makes the following function continuous on (-infinity,infinity). Find the two values of b for which/is a continuous function at x = 2 The one with the greater absolute? value is b = Now draw a graph of f. Sketch the graph of this function and find the following limits, if they exist. (If a limit does not exist, enter DNE.) Let F be the function whose graph is shown below. Evaluate each of the following expressions. (If a limit does not exist or is undefined enter "DNE".)

Explanation / Answer

1.here,for x<-6 ,f(x) = (2x^3+12x^2+8x+48)/(x+6)

                              = 2(x2+4)(x+6)/(x+6)=2(x2+4)

so f(-6-)=2(36+4)=80

now f(x) = -3x2-3x+a at x>=-6

so f(-6+)=-108+18+a=a-90

for a function to be continous f(x+)=f(x-)=f(x) at the point x

so f(-6+)=f(-6-)

a-90=80

so a = 170

2.for the following fuction to be continous f(5-)=f(5+)=f(5)

so cx+9 = cx2-9

5c+9=25c-9

20c=18

c=9/10=.9

3.here f(x) is 7x-8 at x<5 and 3/(x+9) at x>=5

so checking the continuity at x=5

f(5-) should be equal to f(5+) for graph to be continous.

so f(5-)=7*5-8=27

and f(5+)=3/(5+9)=3/14

so as f(5-) is not equal to f(5+) the graph is discontinous at 5.

4.here using the same concept as we used in above parts,

f(5-)-=f(5+)=f(5)

4x-2=-8x+b

18=-40+b

b = 58.

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