Question

if f is a continuous function defined by f(x)={x^2+bx, 5 sin("pie"/2x) then b= ?

Answer 1

I do not understand the { symbol at the beginning and why you have two functions of x, separated by a comma.

Are you asking where the two functions intersect?

Answer 2

Moreover do you really mean
sin("pie"/2x)
or do you mean
sin("pie"x/2)
?

Answer 3

re written:

f(x)= x^2+bx (for all values of x less than or equal to 5)
f(x)= 5 sin ((pie/2)x) (for all values of x greater than 5)

find the value of b

Answer 4

f(x)= x^2+bx (for all values of x less than or equal to 5)
f(x)= 5 sin ((pie/2)x) (for all values of x greater than 5)
-------------------------
If it is continuous then those two functions are the same at x = 5
5^2 + 5b = 5 sin (2.5 pi)
5 + b = sin(2.5 pi)
5 + b = sin (450 degrees) = sin(90) = 1
b = 1-5 = -4

Answer 5

thank you!!