MAT 112 - Calculus: Limits and Continuity

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Limit of a sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Limiting sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Limit of a function at infinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Limit at a point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Further examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Continuity of piecewise-defined functions . . . . . . . . . . . . . . . . . . . . . . . . 16

Links forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Formal definition of a limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

The pinching theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Finding limits using areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

History and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Paradoxes of the infinite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Pi as a limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Infinitesimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Cauchy and Weierstrass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22


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APA

Consults, E. (2022). MAT 112 - Calculus: Limits and Continuity. Afribary. Retrieved from https://afribary.com/works/mat112

MLA 8th

Consults, Education "MAT 112 - Calculus: Limits and Continuity" Afribary. Afribary, 02 Jun. 2022, https://afribary.com/works/mat112. Accessed 09 Aug. 2022.

MLA7

Consults, Education . "MAT 112 - Calculus: Limits and Continuity". Afribary, Afribary, 02 Jun. 2022. Web. 09 Aug. 2022. < https://afribary.com/works/mat112 >.

Chicago

Consults, Education . "MAT 112 - Calculus: Limits and Continuity" Afribary (2022). Accessed August 09, 2022. https://afribary.com/works/mat112