MTH 1110A - Calculus I

• Evaluate two-sided and one-sided limits graphically
• Identify vertical and horizontal asymptotes using limits
• Evaluate the limits of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric, and composite functions analytically
• Determine if a function is continuous at a point by analyzing the three conditions of continuity
• Identify removable, jump, and infinite discontinuities
• Interpret the derivative as instantaneous rate of change and slope of tangent line
• Find the derivative of a function using the limit definition
• Find an equation for a tangent line
• Analyze the behavior of the derivative from the graph of a function, including identifying points of non-differentiability
• Find the derivative of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions
• Determine the appropriate rules to use in differentiating various functions
• Apply basic differentiation rules including power, product, quotient, and chain rules to find derivatives
• Find higher-order derivatives
• Use various notations for derivatives
• Find and interpret the position, velocity, and acceleration of a moving object
• Find derivatives implicitly
• Find a derivative using logarithmic differentiation
• Solve related rates problems
• Find relative extrema using First and Second Derivative tests
• Find absolute extrema on closed, open, and infinite intervals
• Use derivatives to find points of inflection on a curve
• Solve optimization problems
• Use Newton’s method to approximate a zero of a function
• Find the differential of a function and use it to approximate error
• Find the local linear approximation of a function about a point
• Integrate functions involving algebraic, exponential, trigonometric, logarithmic, and inverse trigonometric forms
• Solve an initial value problem
• Evaluate a definite integral by the limit of Riemann sums
• Apply and interpret the Fundamental Theorem of Calculus Part I and Part II
• Evaluate definite integrals by Fundamental Theorem of Calculus
• Evaluate indefinite and definite integrals using the method of substitution
• Find position and velocity functions using integration
• Find displacement and distance traveled using integration

• Precalculus mathematics

• Limits and continuity
• Rates of change, tangent lines, and the definition of derivative
• Derivatives of algebraic, trigonometric, exponential, logarithmic, inverse trigonometric, and composite functions
• Related rates problems
• First and second derivative tests for extrema, curve sketching
• Optimization problems
• Mean Value Theorem
• Newton’s method
• Local linear approximation and differentials
• Definite and indefinite integrals
• Fundamental Theorem of Calculus, Part I and Part II
• Integration by method of substitution
• Rectilinear motion