. Find the constants a and b so that the function f is continuous
on (−∞,+∞)
f(x)={ 2x-1 x≤1
{ ax^3+b 1<x<2
{ x+2b x≥2
at x = 1
2x-1 = a x^3 + b
1 = a + b
at x = 2
a (2)^3 + b = 2 + 2 b
8 a = b + 2
so b =8 a - 2
1 = a + b = 9 a - 2
9 a = 3
a = 1/3
b = 8/3 -6/3 = 2/3
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check
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1 = 1/3 *1+2/3 yes
8/3 + 2/3 = 6/3 + 4/3 yes