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# What value of C would make f(x) continuous at x = 2?

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$$f(x) = \left\{ \begin{array}{c l} \dfrac{-5x^{2}+4x+12}{-3x^{2}+x+10}, & \, x \neq 2 \\ C, & \, x = 2 \end{array} \right.$$

What value of C would make f(x) continuous at x = 2?

• Decimal approximations are not allowed for this problem.
• Compute the exact value for C and express your answer algebraically.
Feb 23, 2022

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Factor  the numerator as   (5x + 6) ( - x + 2)

Factor the denominator as  ( 3x + 5) ( -x + 2)

We are left with

(5x + 6)  /( 3x + 5)

The value of C  that makes this  continuous at x = 2   is     ( 5 (2) + 6)  / (3(2) + 5) =   16 / 11

Feb 23, 2022