Applied Continuity Quiz: Real-World Functions and Limit Reasoning

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| Questions: 15 | Updated: Dec 15, 2025
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1) If a car’s position s(t) is continuous, what real-world fact does this represent?

Explanation

Any subset inherits continuity from the original domain.

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About This Quiz
Applied Continuity Quiz: Real-world Functions And Limit Reasoning - Quiz

Ready to spot induced topology outside the classroom? This quiz shows how restricting attention to smaller regions — like a building, a city district, a race track, or a coastline — creates a new topology shaped by intersections with larger open regions. You’ll explore navigation systems, delivery zones, environmental modeling,... see moreand movement along curves to see how “open sets” change when the space gets smaller. Each scenario helps you understand how subspace topology naturally appears in real-world systems.
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2) The outdoor temperature is modeled as continuous. What does this imply?

Explanation

Extreme Value Theorem ensures max & min on closed intervals.

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3) Which quantities are typically modeled as continuous functions of time?

Explanation

Jump means left and right limits exist but differ.

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4) Oven temp T(t) continuous: T(0)=25, T(10)=200. What follows?

Explanation

Continuity only requires the limit equals the function value.

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5) Continuous fuel-consumption function F(v). Continuity ensures:

Explanation

Reciprocal of a nonzero continuous function is continuous.

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6) River depth rises 2→5 m. Continuity guarantees:

Explanation

Inverse need not be continuous unless function is bijective & monotone.

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7) Why is continuity reasonable for body temperature?

Explanation

Function definition missing → cannot determine continuity.

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8) Profit P(t) continuous. Implications:

Explanation

Only |x|/x has a discontinuity at x=0.

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9) Velocity v(t) continuous. Which scenario matches?

Explanation

Continuous functions on closed intervals are always bounded.

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10) Pollution P(x) continuous on highway. If P(0)=50, P(20)=80:

Explanation

Polynomial limit rule applies directly.

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11) Bridge stress S(x) continuous. Continuity implies:

Explanation

Polynomials are continuous everywhere.

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12) Drone altitude h(t) continuous: 5s=100m,10s=60m. What must be true?

Explanation

Linear functions are continuous everywhere on ℝ.

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13) Medication concentration C(t) continuous. Which ruled out?

Explanation

IVT guarantees a value 4 between f(1)=2 and f(4)=5.

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14) Continuous power-output P(t). Which are guaranteed?

Explanation

Missing definition prevents determining k.

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15) Cost-per-unit C(q). C(100)=20, C(150)=18. What is guaranteed?

Explanation

Continuity requires limit equals function value.

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If a car’s position s(t) is continuous, what real-world fact does...
The outdoor temperature is modeled as continuous. What does this...
Which quantities are typically modeled as continuous functions of...
Oven temp T(t) continuous: T(0)=25, T(10)=200. What follows?
Continuous fuel-consumption function F(v). Continuity ensures:
River depth rises 2→5 m. Continuity guarantees:
Why is continuity reasonable for body temperature?
Profit P(t) continuous. Implications:
Velocity v(t) continuous. Which scenario matches?
Pollution P(x) continuous on highway. If P(0)=50, P(20)=80:
Bridge stress S(x) continuous. Continuity implies:
Drone altitude h(t) continuous: 5s=100m,10s=60m. What must be true?
Medication concentration C(t) continuous. Which ruled out?
Continuous power-output P(t). Which are guaranteed?
Cost-per-unit C(q). C(100)=20, C(150)=18. What is guaranteed?
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