CALCULUS PROBLEMS LIST

Beginning Differential Calculus :

• Problems on the
  • limit of a function as x approaches a fixed constant
  • limit of a function as x approaches plus or minus infinity
  • limit of a function using the precise epsilon/delta definition of limit
  • limit of a function using L'Hopital's Rule
• Problems on the continuity of a function of one variable
• Problems on the "Squeeze Principle"
• Problems on the limit definition of the derivative
• Problems on the chain rule
• Problems on the product rule
• Problems on the quotient rule
• Problems on differentiation of trigonometric functions
• Problems on differentiation of inverse trigonometric functions
• Problems on detailed graphing using first and second derivatives
• Problems on applied maxima and minima
• Problems on implicit differentiation
• Problems on related rates
• Problems on logarithmic differentiation
• Problems on the differential
• Problems on the Intermediate-Value Theorem
• Problems on the Mean Value Theorem

Beginning Integral Calculus :

• Problems using summation notation
• Problems on the limit definition of a definite integral
• Problems on u-substitution
• Problems on integrating exponential functions
• Problems on integrating trigonometric functions
• Problems on integration by parts
• Problems on integrating certain rational functions, resulting in logarithmic or inverse tangent functions
• Problems on integrating certain rational functions by partial fractions
• Problems on power substitution
• Problems on integration by trigonometric substitution
• Problems on area
• Problems on volume by disc method
• Problems on volume by shell method
• Problems on volume by cross-sectional area
• Problems on moment, mass, center of mass, and centroid
• Problems on kinetic energy
• Problems on work
• Problems on force of water pressure
• Problems on arc length
• Problems on surface area
• Problems on Pappus' Theorem

Sequences and Infinite Series :

Multi-Variable Calculus :

• Problems on partial derivatives
• Problems on the chain rule
• Problems on critical points and extrema for
  • unbounded regions
  • bounded regions
• Problems on double integrals using
  • rectangular coordinates
  • polar coordinates
• Problems on triple integrals using
  • rectangular coordinates
  • cylindrical coordinates
  • spherical coordinates