calculus help?

Question

Locate the discontinuities of the function.
y= 3/(7+e^7/x)

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For what value of the constant c is the function f continuous on (-infinity, infinity )?

f(x) = { cx^2 + 2x if x < 3 }
{ x^3 - cx if x greathan or equal to 3 }


help please & thank you in advance.

Answer 1

Discontinuity occurs when the function is not defined, or does not take the same value when approached from below, above, and at, that location.
For case (1) obviously y is not defined at x = 0. So x = 0 is the discontinuous point of the function.
For case (2) We have to let:
c(3)^2 + 2*3 = (3)^3 - c*3
or 12c = 21
so: c = 7/4