Applied Continuity Quiz: Real-World Functions And Limit Reasoning

1) If a car’s position s(t) is continuous, what real-world fact does this represent?

Car teleports

Moves without jumps

Must be constant speed

Car cannot stop

Any subset inherits continuity from the original domain.

Explanation

Any subset inherits continuity from the original domain.

2) The outdoor temperature is modeled as continuous. What does this imply?

Sudden spikes

Never decreases

Smooth changes

Linear trend

Extreme Value Theorem ensures max & min on closed intervals.

Explanation

Extreme Value Theorem ensures max & min on closed intervals.

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

Water level

Bus passengers

Tree height

Air pressure

Jump means left and right limits exist but differ.

Explanation

Jump means left and right limits exist but differ.

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

Temp =150 at some time

Stayed constant

Instant jump

Temp decreased

Continuity only requires the limit equals the function value.

Explanation

Continuity only requires the limit equals the function value.

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

Tiny changes→tiny fuel changes

Spikes

Graph has no jumps

Same fuel at all speeds

Reciprocal of a nonzero continuous function is continuous.

Explanation

Reciprocal of a nonzero continuous function is continuous.

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

Stayed 2

Jumped to 5

Passed all depths

Must decrease

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

Explanation

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

7) Why is continuity reasonable for body temperature?

Spike abruptly

Cannot change instantly

Thermometer adds discontinuity

Always constant

Function definition missing → cannot determine continuity.

Explanation

Function definition missing → cannot determine continuity.

8) Profit P(t) continuous. Implications:

No instant jumps

Gradual changes

Large jumps allowed

No gaps

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

Explanation

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

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

Instant 10→40

Gradual changes

Teleportation

Constant speed

Continuous functions on closed intervals are always bounded.

Explanation

Continuous functions on closed intervals are always bounded.

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

Pollution=65 somewhere

Decreases

Constant

Jumps

Polynomial limit rule applies directly.

Explanation

Polynomial limit rule applies directly.

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

Stress gradual

No infinite spikes

Jump 1000→5000

All stress levels appear

Polynomials are continuous everywhere.

Explanation

Polynomials are continuous everywhere.

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

Hovered at 80

Only upward

Only downward

Constant

Linear functions are continuous everywhere on ℝ.

Explanation

Linear functions are continuous everywhere on ℝ.

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

Increase

Decrease slowly

Instant double

Peak then stabilize

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

Explanation

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

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

No jumps

Includes intermediates

Must increase

No gaps

Missing definition prevents determining k.

Explanation

Missing definition prevents determining k.

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

Cost=19 somewhere

Linear

Constant

Stop at 120

Continuity requires limit equals function value.

Explanation

Continuity requires limit equals function value.

Applied Continuity Quiz: Real-World Functions and Limit Reasoning

1) If a car’s position s(t) is continuous, what real-world fact does this represent?

2)

What first name or nickname would you like us to use?

2) The outdoor temperature is modeled as continuous. What does this imply?

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

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

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

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

7) Why is continuity reasonable for body temperature?

8) Profit P(t) continuous. Implications:

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

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

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

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

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

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

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