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Posts Tagged ‘limits’

(A Comic Guide to Limits) Part 1 – When Limits Exist

November 10th, 2009 Mr. H 9 comments

I do something similar to this when I introduce limits. It gives students a practical understanding of what limits are and how to evaluate them.

If you see glaring mistakes, please let me know.

Part 1 – When Limits Exist

Categories: comic, math Tags: , , , ,

Importance of Definitions (Zero)

October 16th, 2009 Mr. H No comments

Evaluate the following and justify your solution

If latex does not display properly (you might have to enable javascript) or if you’re reading from Google Reader skip to the text version

  1. 0^0 =
  2. \mathop {\lim }\limits_{x\to 0} x^0 =
  3. \mathop {\lim }\limits_{x\to 0} 0^x =
  4. \mathop {\lim }\limits_{x\to 0} x^x =
  5. \frac{0^a}{0^a} =
  6. 0^{a-a} =
  7. \frac{a^0}{a^0} =
  8. a^{0-0} =
  9. \mathop {\lim }\limits_{x\to 0} \frac{x^a}{x^a} =
  10. 0^\infty =
  11. \mathop {\lim }\limits_{x\to 0} 0^{\frac{1}{x}} =
  12. \mathop {\lim }\limits_{x\to 0} \sqrt[x]{0} =
  13. \mathop {\lim }\limits_{x\to 0} x^{\frac{1}{x}} =
  14. \mathop {\lim }\limits_{x\to 0} \sqrt[x]{x} =
  15. If 0^0=a, what is log_{0}a=
  16. If 0^0=a, what is \mathop {\lim }\limits_{x\to 0} log_{x}a=
  17. If 0^0=a, what is \sqrt[0]{a}=
  18. If 0^0=a, what is \mathop {\lim }\limits_{x\to 0} \sqrt[x]{a}=

Text Version

  1. What is zero to the zeroth power? What is zero raised to the power of zero?
  2. What is the limit as x approaches zero of x to the zeroth power?
  3. What is the limit as x approaches zero of zero to the x power?
  4. What is the limit as x approaches zero of x to the xth power?
  5. What is zero to the power of a divided by zero to the power of a?
  6. What is zero to the power of the quantity a minus a?
  7. What is a to the power of zero divided by a to the power of 0?
  8. What is a to the power of the quantity 0 minus 0?
  9. What is the limit as x approaches zero of x to the power of a divided by x to the power of a?
  10. What is zero to the infinity power?
  11. What is the limit as x approaches zero of zero to the power of one divided by x?
  12. What is the limit as x approaches zero of xth power of zero?
  13. What is the limit as x approaches zero of x to the power of one divided by x?
  14. What is the limit as x approaches zero of xth power of x?
  15. If zero to the zeroth power is equal to a, what is log base zero of a?
  16. If zero to the zeroth power is equal to a, what is the limit as x approaches zero of log base x of a?
  17. If zero to the zeroth power is equal to a, what is zeroth root of a?
  18. If zero to the zeroth power is equal to a, what is the limit as x approaches zero of xth root of a?
Categories: math Tags: , , , , , , , , , , , ,