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How do you find the constants a and b such that the function is continuous on the entire real line for f(x)={x^3, x≤2 and ax^2, x>2



Answer :

crisforp
[tex] \lim_{x \to 2} f(x) = f(2)[/tex]

In your case, 2^3 = a * 2^2 <=> 8 = a * 4 <=> a = 8 / 4 <=> a = 2.

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