Question

find b, f(x)={x-b/b+1,x<0 x^2 +b, x>=0 is continuous at x=0
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Answer 1

Step-by-step explanation:

x-->0+, x=0+h where h is smallest positive value then

f(x)=x^2+b

f(0+h)= h^2+b --A

x-->0-, x = 0-h where h is smallest positive value then

f(x) = x-b/b+1

f(0-h)=-h-b/b+1 --B

for f(x) to be continuous A=B

h^2+b=(h-b)/b+1

h^2b+b^2+h^2+b= h-b

b^2+b(h^2+2)+h^2=0

b=-(h^2+2)+/-sqrt((h^2+2)^2-4×1×h^2)/2

hope this helps