Topics › Calculus › Test Continuity at a Point — Three-Part Definition

Calculus · LIM

Test Continuity at a Point — Three-Part Definition

f is continuous at c iff: (1) f(c) exists, (2) lim_{x→c} f(x) exists, (3) lim_{x→c} f(x) = f(c).

CalculusCommon Core LIM-2.CLIMVerified correct ✓

Worked examples

Let f(x) = { 3x + -3 if x < 1 { 5 if x ≥ 1. Is f continuous at x = 1? Enter 1 for yes, 0 for no.
Answer: 0

Let f(x) = { 3x + 2 if x < -3 { -4 if x ≥ -3. Is f continuous at x = -3? Enter 1 for yes, 0 for no.
Answer: 0

Every problem on Pounce is generated and checked by code — never a wrong answer key.

Master Test Continuity at a Point — Three-Part Definition

Code-verified problems at exactly the right level, explained the way your kid learns.

Start your free trial 🐾

Build up to this

Evaluate Limits Algebraically — Substitution and Factoring Continuity — Definition and Types of Discontinuity

More Calculus topics

Evaluate Limits Algebraically — Substitution and Factoring Evaluate Trigonometric Limits — sin(x)/x as x→0 Limits at Infinity — End Behavior of Rational Functions Derivative from the Limit Definition Power Rule — Differentiate Polynomial Functions Product Rule — Differentiate a Product of Two Functions Chain Rule — Differentiate Composite Functions Derivatives of Trig Functions — sin, cos, tan