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Calc 1 HW #1

# Calc 1 HW #1 - lim x →∞ 7 x-3 x 2-6 = 1 11 Without...

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1016 231 Calculus I for Engineering Technologists Homework #1 - Limits (Due Friday, Dec 16) For questions #1-3, recall that a function is discontinuous at x = a if one of three things happens: 1) f ( a ) is undefined, 2) lim x a f ( x ) does not exist, or 3) if f ( a ) 6 = lim x a f ( x ). 1. The function f ( x ) = 2 x 2 - 2 x x 2 - 1 is discontinuous at x = - 1. Which of the three conditions does it fail? Justify your answer. 2. The function f ( x ) = ( 1 2 x + 4 , x < 2 4 - 3 x, x 2 is discontinuous at x = 2. Which of the three conditions does it fail? Justify your answer. 3. The function f ( x ) ( x 2 +6 x - 7 x - 1 , x 6 = 1 4 x = 1 is discontinuous at x = 1. Which of the three conditions does it fail? Justify your answer. Evaluate the following limits. If the limit Does Not Exist, then provide as much information as you can about the functions behavior. You must justify your answer with sound mathematical reasoning. 4. lim x →- 2 x 2 - 4 x + 2 = 5. lim x →- 2 x - 4 x + 2 = 6. lim x 5 3 - x ( x - 5) 2 = 7. lim x 5 x 2 ( x - 5) 2 = 8. lim x →∞ 3 x 6 - 5 x 3 + 2 x 6 x 6 + 9 x 2 = 9. lim x →-∞ x 2 x - 5 =

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Unformatted text preview: lim x →∞ 7 x-3 x 2-6 = 1 11. Without using a graphing calculator, or any other graphing software, describe (in words) the behavior of y = 5-1 x 2 and sketch a rough graph. 12. Without using a graphing calculator, or any other graphing software, describe (in words) the behavior of y = 5-1 1+ x 2 and sketch a rough graph. 13. Without using a graphing calculator, or any other graphing software, describe (in words) the behavior of y = 5-x 1+ x 2 and sketch a rough graph. 14. Without using a graphing calculator, or any other graphing software, describe (in words) the behavior of y = 5-x 2 1+ x 2 and sketch a rough graph. 15. Without using a graphing calculator, or any other graphing software, describe (in words) the behavior of the function below and sketch a rough graph. y = 6 1 + 2 x 2...
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Calc 1 HW #1 - lim x →∞ 7 x-3 x 2-6 = 1 11 Without...

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