math/Calc

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g(x)={1+cos(pi/2-x/1)
0

for-2 <or= x <or=2
for x<2 or x>2

is g(x) continuous at x=2 is it differentiable at x=2? ex[lain in detail I'm very confused as to how to solve this problem

  • math/Calc -

    As written, it appears that
    g(x) = 1+cos(pi/2 - x) = 1+sin(x)...

    At x=2, that would make g(2) = 1+sin(2)

    since g(2) is not 0, g is not continuous at x=2, since g(x)=0 for x>2.

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