if the following is continuous, what is a

Question

h(t)={2t+b if t<0

{2cos(t)-3 if 0< or equal to t < or equal to pi/2

{asin(t)+5b if t>pi/2

Answer 1

You need to find "b" first, by guaranteeing continuity at 0.

 

THEN you need to find "a" by guaranteeing continuity at pi/2.   [a being the coefficient in the third piece of the function]

Answer 2

Set the first part equal to the 2nd part to find b.

 

2t + b = 2cos(t) - 3

 

This is true at t=0.  Therefore,

 

b = 2 - 3 

b= -1

 

 

Now we set the 2nd part equal to the 3rd part at t=π/2, and using the value of b we just found.

 

2cos(π/2) - 3 = asin(π/2) + 5(-1)

 

-3 = a - 5

 

2 = a