A function f is defined as follows:(adsbygoogle = window.adsbygoogle || []).push({});

f(x) = 2cos(x) if x≤c,

= ax^2 + b if x > c .

Where a,b, and c are constants. If b and c are given. find all values of a for which f is continous at the point x = c

Solution:

a = (2cos(c) - b)/c^2 if c ≠ 0 ; if c = 0 there is no solution unless b = 2.

I dont understand how if c = 0 and b = 2 there is a solution at c = 0

For instance... (2cos(c) - 2)/c^2 = (2/c)( Cos(c) - 1 )/c = 2/0*0 as c → 0 which is still a discontinuity.

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# Continuity Question

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