Compute Limits, Derivatives, Linear Approximations, And Integrals Using Various Techniques

Compute Limits, Derivatives, Linear Approximations, And Integrals Using Various Techniques.

Calculus I (MATH105)

Elementary functions, limits, continuity, limits involving infinity, tangent lines, derivative of elementary functions, differentiation rules, chain rule, implicit differentiation, linear approximation, l`Hospital rule. Graph sketching (extrema, intervals of monotonicity, concavity), optimization. Antiderivatives, definite integrals, Fundamental Theorem of Calculus, integration by substitution, area between curves, improper integrals.

Learning Outcomes

At the end of the course, students will be able to :

  1. Apply Calculus To Geometry And To Real World Problems (Such As Graph Sketching, Optimization, Related Rates, Area Computation).
  2. Compute Limits, Derivatives, Linear Approximations, And Integrals Using Various Techniques.
  3. Explain Some Important Concepts Of Calculus (Such As Limit, Continuity, Derivative And Integral).
  4. Justify Some General Results In Single-Variable Calculus From A Theoretical Point Of View.
  5. Use Technology To Investigate Limits, Graphs, And Integrals.
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