π Quick formula sheet (open before the quiz)
- Continuity at a (3 conditions): (1) f(a) is defined, (2)
lim f(x)exists as xβa, (3)lim f(x) = f(a). - Types of discontinuity: removable (limit exists, but β f(a) or f(a) undefined), jump (left β right limit), infinite (limit β Β±β), oscillating.
- Continuous on their domains: polynomials, rational functions, |x|, βx, eΛ£, ln x, sin x, cos x, tan x. Sums, products, compositions and quotients (denominator β 0) of continuous functions are continuous.
- Continuity on [a,b]: continuous on (a,b), right-continuous at a, left-continuous at b.
- IVT: f continuous on [a,b] and N between f(a) and f(b) βΉ f(c) = N for some c in (a,b). Sign change βΉ a root.
- EVT: f continuous on [a,b] βΉ f has an absolute max and min there. Differentiable βΉ continuous, but not the reverse.
πΊ Learn more
πΊ To learn any topic in detail, watch our free lectures and read the notes on our website mformathodology.com and on our YouTube channel @MforMATHODOLOGY.
Instructor: Rabbia Abid Khan Β· MforMathodology