User:Igor Nazarov/Calculus 1

Introduction

• function (mathematics)
  • domain (mathematics)
  • range (mathematics)
• graph of a function
• examples
  • constant function
  • linear function
  • quadratic polynomial
  • polynomial
  • power function
    • n-th root
  • trigonometric functions
    • sine, cosine, tangent
  • exponential function
  • piecewise functions
    • absolute value
  • inverse functions
  • logarithmic function
    • natural logarithm
  • inverse trigonometric functions
• some applications
  • exponential growth and exponential decay

Limits

• limit
  • one-sided limits
  • when limits do not exist
  • limit laws
• squeeze theorem
• 0/0 uncertainty, cancellation of the division by zero
  • factorization of polynomials
  • square roots and conjugates
  • $\lim _{x\to 0}{\frac {\sin x}{x}}$
• limits at infinity and infinite limits
• Continuous function
  • discontinuity (mathematics)