Foundations: Limits and Continuity

Develop an intuitive understanding of the limit concept through graphical and numerical exploration.

Determine one-sided limits and use them to establish whether a two-sided limit exists.

Apply the Squeeze (Sandwich) theorem to evaluate complex limits.

Evaluate limits involving standard trigonometric, exponential, and logarithmic forms.

Evaluate limits of indeterminate forms like 1^infinity, 0^0, and infinity^0 using logarithmic manipulation.

Define continuity at a point and over an interval using limits, and classify types of discontinuities (removable, jump, infinite).

Apply the Intermediate Value Theorem to establish the existence of roots for continuous functions.