Continuity problem?

Question

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Sorry for so many questions. I've been solving a mass amount of random problems from my textbook to prepare for a test.

For what value(s) of the constant c is the following function continuous on $$(-\infty,\infty)$$ ?

$$f(x)=$$ $$\left\{cx^{2}+2x, x<2$$

$$\left\{x^{3}-cx, x\geq2$$

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The function in the original problem had both the equations all in one bracket. Bear with me and my LaTeX noobiness lol

chilledz3non Sep 20, 2014

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Best Answer

$$cx^2+2x=x^3-cx\qquad $for $ x=2$$

sub in x=2 and solve the equation for c

$$\\4c+4=8-2c\\
6c=4\\
c=2$$

Melody Sep 20, 2014

Melody · Answer 1 · 2014-09-20T07:43:08

$$cx^2+2x=x^3-cx\qquad $for $ x=2$$

sub in x=2 and solve the equation for c

$$\\4c+4=8-2c\\
6c=4\\
c=2$$

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chilledz3non · Answer 2 · 2014-09-20T07:59:35

Thanks so much Melody :D