Calculus MTH 250 Lecture 7 Previous Lectures Summary
- Slides: 32
Calculus (MTH 250) Lecture 7
Previous Lecture’s Summary • Limits by definition • Formal definition of one-sided limits • Comparison theorem • Sandwich theorem • Golden rules for limits • Introduction to continuity • Discontinuity • Piecewise continuous functions • Continuous extension • Intermediate value theorem
Today’s Lecture • Formal definition of continuity • Important results of continuity • Hyperbolic trigonometric functions • Inverse hyperbolic trigonometric functions • Boundedness of continuous functions • Uniform continuity • Tangent lines
Formal definition of continuity
Important continuity results
Important continuity results Exponential functions are continuous everywhere since
Important continuity results Sine and Cosine functions are continuous everywhere since
Important continuity results
Important continuity results
Important continuity results
Important continuity results
Important continuity results Example: |x| is continuous everywhere.
Important continuity results
Hyperbolic functions
Hyperbolic functions •
Inverse hyperbolic functions
Inverse hyperbolic functions
Inverse hyperbolic functions
Inverse hyperbolic functions
Boundedness of continuous functions
Boundedness of continuous functions
Boundedness of continuous functions
Boundedness of continuous functions
Uniform continuity
Tangent lines
Tangent lines
Tangent lines
Tangent lines
Tangent lines Example: Find the tangent line to
Tangent lines Example
Tangent lines
Lecture Summary • Formal definition of continuity • Important results of continuity • Hyperbolic trigonometric functions • Inverse hyperbolic trigonometric functions • Boundedness of continuous functions • Uniform continuity • Tangent lines
- Mth 210
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