exam 16
question 1: standard g.gmd.1
what is a limit?
a. how much math you can handle
b. a function that has no end
c. when we approach a value but never touch it
d. the area under a curve
question 2: standard g.gmd.1
what is an asymptote?
a. a line that is never touched
b. the x intercept
c. a perpendicular line that bisects a shape
d. a regular polygon
question 3: standard g.gmd.1
what is the formula for area of circle?
a. $a = r^2$
b. $a = \text{base} \times \text{height}$
c. $a = \pi r^2$
d. $a = \text{length} \times \text{width} \times \text{height}$
question 4: standard g.gmd.1
how does a n - sided polygon help us find the area of a circle?
a. it allows us to get close to the limit (edge) of the circle and add up shapes that we do know the area for to approximate the area of a circle
b. it helps us create the formula for area of a circle by using pi
c. its a way to measure the volume of a circle
d. allows us to use geometric proofs to determine the approximate area of a circle
question 5: standard g.gmd.1
which polygon would most closely resemble a circle in terms of area?
a. pentagon
b. square
c. hexagon
d. 120 - gon

Question

exam 16
question 1: standard g.gmd.1
what is a limit?
  a. how much math you can handle
  b. a function that has no end
  c. when we approach a value but never touch it
  d. the area under a curve
question 2: standard g.gmd.1
what is an asymptote?
  a. a line that is never touched
  b. the x intercept
  c. a perpendicular line that bisects a shape
  d. a regular polygon
question 3: standard g.gmd.1
what is the formula for area of circle?
  a. $a = r^2$
  b. $a = \text{base} \times \text{height}$
  c. $a = \pi r^2$
  d. $a = \text{length} \times \text{width} \times \text{height}$
question 4: standard g.gmd.1
how does a n - sided polygon help us find the area of a circle?
  a. it allows us to get close to the limit (edge) of the circle and add up shapes that we do know the area for to approximate the area of a circle
  b. it helps us create the formula for area of a circle by using pi
  c. its a way to measure the volume of a circle
  d. allows us to use geometric proofs to determine the approximate area of a circle
question 5: standard g.gmd.1
which polygon would most closely resemble a circle in terms of area?
  a. pentagon
  b. square
  c. hexagon
  d. 120 - gon

Accepted Answer

### Question 1
# Brief Explanations:
To determine the correct definition of a limit, we analyze each option:
- Option a: "How much math you can handle" is incorrect as it refers to a person's capacity, not a mathematical limit.
- Option b: "A function that has no end" describes an infinite function, not a limit.
- Option c: "When we approach a value but never touch it" accurately defines a limit in calculus, where a function approaches a value as the input gets closer to a point without necessarily reaching it.
- Option d: "The area under a curve" refers to an integral, not a limit.

# Answer:
c. When we approach a value but never touch it

### Question 2
# Brief Explanations:
For the definition of an asymptote:
- Option a: "A line that is never touched" is correct. An asymptote is a line that a graph approaches but never intersects (for vertical/horizontal asymptotes in most cases, or approaches as a slant asymptote).
- Option b: "The x intercept" is where a graph crosses the x - axis, not an asymptote.
- Option c: "A perpendicular line that bisects a shape" describes a perpendicular bisector, not an asymptote.
- Option d: "A regular polygon" is a closed geometric figure with equal sides and angles, not related to an asymptote.

# Answer:
a. A line that is never touched

### Question 3
# Brief Explanations:
The formula for the area of a circle:
- Option a: $A = r^{2}$ is missing the $\pi$ factor, so it's incorrect.
- Option b: $A=\text{base}\times\text{height}$ is the formula for the area of a parallelogram (including rectangles and triangles in some cases), not a circle.
- Option c: $A=\pi r^{2}$ is the correct formula for the area of a circle, where $r$ is the radius.
- Option d: $A = \text{length}\times\text{width}\times\text{height}$ is the formula for the volume of a rectangular prism, not the area of a circle.

# Answer:
c. $A = \pi r^{2}$

### Question 4
# Brief Explanations:
How an $n$ - sided polygon helps find the area of a circle:
- Option a: "It allows us to get close to the limit (edge) of the circle and add up shapes that we do know the area for to approximate the area of a circle" is correct. By inscribing or circumscribing an $n$ - sided polygon around a circle and increasing $n$, we can approximate the circle's area by summing the areas of the polygon's sides (which are triangles in the case of a regular polygon).
- Option b: "It helps us create the formula for area of a circle by using pi" is not the main way an $n$ - sided polygon is used to find the area of a circle. The formula for the area of a circle is derived from the limit of the polygon's area as $n\to\infty$, not just by using $\pi$ directly with the polygon.
- Option c: "Its a way to measure the volume of a circle" is incorrect as a circle is a two - dimensional figure and has no volume.
- Option d: "Allows us to use geometric proofs to determine the approximate area of a circle" is not as accurate as option a. The key idea is using the limit of the polygon's area as $n$ increases, not just geometric proofs in general.

# Answer:
a. It allows us to get close to the limit (edge) of the circle and add up shapes that we do know the area for to approximate the area of a circle

### Question 5
# Brief Explanations:
Which polygon most closely resembles a circle in terms of area:
- As the number of sides $n$ of a regular polygon increases, the polygon becomes more and more like a circle. Among the options, a 120 - gon (option d) has more sides than a pentagon (5 sides), square (4 sides), or hexagon (6 sides). So, a 120 - gon will be the closest to a circle in terms of area.
- Option a: A pentagon has only 5 sides and is far from the shape of a circle.
- Option b: A square has 4 sides and is not close to a circle.
- Option c: A hexagon has 6 sides and is closer than a square or pentagon but not as close as a 120 - gon.

# Answer:
d. 120 - gon

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