Lesson 1 and 2

• LIMITS


  • Strategy for making confident predictions
• When Algebra alone is insufficient in solving a problem, you can use Calculus
• Tools used in Calculus

  • LIMITS
  • DERIVATIVES
  • INTEGRAL
• Deriatives


  They are build from Limits
• Integral


  It gives the inverse form of deriatives.
• Lim f(x) = L read as ‘‘The limit of f(x) as x approaches c is L.”
• f(x)


  It is the function defined at every number (x)
• APPROACHING


  It means an unlimited degree of closeness that no other value stands between f(x) and the limit.
• → 


  symbol for approaching
• c


  symbol for any real number
• L


  symbol for limit
• 1 Table of values

  2 Substitution method

  3 Graphing


  3 Ways to estimate the limit
• Limits where the values just explode unlimitedly; each one-sided limit does not exist; and there is no number to which f(x) can be made as close as we want, whether from the right or from the left.

  INFINITE LIMITS
• Two types of One-sided limits

  1. The limit of f(x) as x approaches a from the right
  2. The limit of f(x) as x approaches a from the left
• CALCULUS


  It is a branch of mathematics that deals with rate of change and motion
• It is a branch of mathematics that deals with rate of change and motion

  CALCULUS
• THEOREM: LIMITS OF THE CONSTANT

  
• THEOREM: LIMIT OF THE IDENTITY

  
• THEOREM: LIMIT OF A CONSTANT MULTIPLE OF A FUNCTION

  
• THEOREM: LIMIT OF A POWER OF A FUNCTION

  
• THEOREM: LIMIT OF A POLYNOMIAL FUNCTION

  
• THEOREM: LIMIT OF A RATIONAL FUNCTION

  
• THEOREM: LIMIT OF A RADICAL/ROOT OF A FUNCTION

  
• When direct substitution of the constant c gives an indeterminate number. The limit can be evaluated by first simplifying the rational function using factoring method, and then directly substituting c.
• a pair of sums/differences Involving radicals whose product does not involve radicals anymore.

  Conjugates