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aalyn [17]
2 years ago
5

Is the function continuous at x = -17

Mathematics
1 answer:
Pavlova-9 [17]2 years ago
3 0

For a function to be continuous at an x-value, say -17, you need to make sure two things line up:

The limit from the left equals the limit from the right.

     \lim_{x \to -17^{-}} f(x) =  \lim_{x \to -17^{+}} f(x)

This limit equals the functions value.

    \lim_{x \to -17} f(x) = f(-17)

The left hand limit involves the first piece, f(x) = 20x + 1:

    \begin{aligned} \lim_{x \to -17^{-}} f(x) &=  \lim_{x \to -17^{-}} (20x+1)\\[0.5em]&=   20(-17)+1\\[0.5em]&=   -339\endaligned}

The right hand limit invovles the second piece, f(x) = -10x^2:

    \begin{aligned} \lim_{x \to -17^{+}} f(x) &=  \lim_{x \to -17^{+}} (-10x^2)\\[0.5em]&=   -10\cdot (-17)^2\\[0.5em]&=   -2890\endaligned}

Since the two one-sided limits don't match, the function is not continuous at x=-17.

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  2. Set:                                                                                                                     \displaystyle 6x + 18 < 3(3x)
  3. Factor:                                                                                                               \displaystyle 3(2x + 6) < 3(3x)
  4. [Division Property of Equality] Divide 3 on both sides:                                  \displaystyle 2x + 6 < 3x
  5. [Subtraction Property of Equality] Subtract 3x on both sides:                       \displaystyle -x + 6 < 0
  6. [Subtraction Property of Equality] Subtract 6 on both sides:                        \displaystyle -x < -6
  7. [Division Property of Equality] Divide -1 on both sides:                                 \displaystyle x > 6
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