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(MTH 250)

(MTH 250). Calculus. Lecture 4. Previous Lecture’s Summary. Symmetry test Algebraic operations on functions Composition of functions Trigonometric functions Inverse of a function Domain and range of inverse functions Horizontal line test. Today’s Lecture. Logarithmic functions.

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(MTH 250)

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  1. (MTH 250) Calculus Lecture 4

  2. Previous Lecture’s Summary • Symmetry test • Algebraic operations on functions • Composition of functions • Trigonometric functions • Inverse of a function • Domain and range of inverse functions • Horizontal line test

  3. Today’s Lecture • Logarithmic functions. • Inverse trigonometric functions • Introduction to limits • One sided limits • Limits that don’t exist • Vertical asymptotes • Laws of limit

  4. Logarithmic functions

  5. Logarithmic functions

  6. Logarithmic functions

  7. y x Inverse trigonometric functions y = sinx y = sin–1x

  8. y y = sin–1x y = sin–1x x –1 –1 1 1 y 1 x –1 Inverse trigonometric functions y = sinx

  9. y y = cos–1x x 0 –1 1 Inverse trigonometric functions

  10. Inverse trigonometric functions

  11. Inverse trigonometric functions

  12. Introduction to limits

  13. Introduction to limits

  14. Introduction to limits

  15. One sided limits

  16. One sided limits

  17. One sided limits

  18. One sided limits

  19. One sided limits

  20. Limits that don’t exist

  21. Limits that don’t exist

  22. Limits that don’t exist 2 1 1 2 3 4

  23. Limits that don’t exist

  24. Limits that don’t exist

  25. Vertical Asymptotes

  26. Vertical Asymptotes vertical asymptote at x=0.

  27. Vertical Asymptotes

  28. Laws of limits

  29. Laws of limits

  30. Laws of limits

  31. Laws of limits

  32. Laws of limits

  33. Laws of limits

  34. Lecture Summary • Logarithmic functions. • Inverse trigonometric functions • Introduction to limits • One sided limits • Limits that don’t exist • Vertical asymptotes • Laws of limit

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