CALCULUS AND ITS APPLICATIONS
COMPREHENSIVE EXAM 2026 FULL PROBLEMS
AND CORRECT ANSWERS
◉ Limit of a Function. Answer: Value function approaches as inputs
approach a point.
◉ Continuity. Answer: Function is continuous if limits equal function
value.
◉ Partial Differentiation. Answer: Derivatives of functions with respect
to one variable.
◉ Chain Rule. Answer: Method for differentiating composite functions.
◉ Jacobian. Answer: Matrix of first-order partial derivatives.
◉ Tangent Plane. Answer: Plane that touches a surface at a point.
◉ Normal Line. Answer: Line perpendicular to the tangent plane.
, ◉ Extreme Values. Answer: Maximum or minimum values of a
function.
◉ Lagrange's Multiplier. Answer: Method for finding extrema with
constraints.
◉ Taylor Series. Answer: Expansion of functions into infinite series.
◉ Maclaurin Series. Answer: Taylor series centered at zero.
◉ Functions of Several Variables. Answer: Functions depending on two
or more independent variables.
◉ Direct Substitution. Answer: Evaluating limits by substituting values
directly.
◉ Indeterminate Form. Answer: Expression that does not have a clear
limit.
◉ Path Method. Answer: Evaluating limits by approaching along
different paths.
◉ Limit Definition. Answer: Formal definition using epsilon-delta
criteria.
COMPREHENSIVE EXAM 2026 FULL PROBLEMS
AND CORRECT ANSWERS
◉ Limit of a Function. Answer: Value function approaches as inputs
approach a point.
◉ Continuity. Answer: Function is continuous if limits equal function
value.
◉ Partial Differentiation. Answer: Derivatives of functions with respect
to one variable.
◉ Chain Rule. Answer: Method for differentiating composite functions.
◉ Jacobian. Answer: Matrix of first-order partial derivatives.
◉ Tangent Plane. Answer: Plane that touches a surface at a point.
◉ Normal Line. Answer: Line perpendicular to the tangent plane.
, ◉ Extreme Values. Answer: Maximum or minimum values of a
function.
◉ Lagrange's Multiplier. Answer: Method for finding extrema with
constraints.
◉ Taylor Series. Answer: Expansion of functions into infinite series.
◉ Maclaurin Series. Answer: Taylor series centered at zero.
◉ Functions of Several Variables. Answer: Functions depending on two
or more independent variables.
◉ Direct Substitution. Answer: Evaluating limits by substituting values
directly.
◉ Indeterminate Form. Answer: Expression that does not have a clear
limit.
◉ Path Method. Answer: Evaluating limits by approaching along
different paths.
◉ Limit Definition. Answer: Formal definition using epsilon-delta
criteria.
