🔵 1.1 Limits of Functions Using Numerical and Graphical Techniques | Instruction Day 2 of 2

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3 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

This unit is aligned to the AP Calculus CED as well as the textbook Calculus for the AP Course 4th Ed Sullivan/Miranda

Question 1

01:28

Ɛhia

Question 2

02:06

Ɛhia

Question 3

04:51

Ɛhia

Question 1

01:28

Ɛhia

Asemmisa {{asɛmmisaAhyɛnsode}}

A student looks at the graph of the piecewise function and notes that and
What is the correct conclusion regarding the overall limit , and why?

The overall limit is 0.5 because it is the average of the two one-sided limits.

The overall limit does not exist (DNE) because the left-hand and right-hand limits approach two different finite values.

The overall limit exists and is equal to 0 because the function starts at the origin.

The overall limit is 1 because the right-hand limit takes precedence on a standard coordinate plane.

Question 2

02:06

Ɛhia

Asemmisa {{asɛmmisaAhyɛnsode}}

Consider the function
. Why do are we required to use a one-sided limit instead of a two-sided limit when investigating the behavior of the function as x approaches 1?

Approaching from the right is just a shortcut to finding the y-intercept.

The function is not defined for x less than 1, so it's impossible to approach 1 from the left.

The left-hand limit would automatically equal infinity, which is too difficult to graph.

Square root functions can only ever be evaluated using right-hand limits.

Question 3

04:51

Ɛhia

Asemmisa {{asɛmmisaAhyɛnsode}}

Which of the following is the most mathematically sound practice when using a graph to investigate a limit?

Assume the limit does not exist if the graph requires you to change the default zoom settings.

Treat the graph as a helpful visual hypothesis, but verify the behavior using algebraic properties or numerical tables.

Only look at the graph from a zoomed out perspective where the entire domain is visible at once.

Trust the first visual output you see, as modern graphing software doesn't make mistakes.

Asemmisa {{asɛmmisaAhyɛnsode}}

A student looks at the graph of the piecewise function and notes that and
What is the correct conclusion regarding the overall limit , and why?

The overall limit is 0.5 because it is the average of the two one-sided limits.

The overall limit does not exist (DNE) because the left-hand and right-hand limits approach two different finite values.

The overall limit exists and is equal to 0 because the function starts at the origin.

The overall limit is 1 because the right-hand limit takes precedence on a standard coordinate plane.

Asemmisa {{asɛmmisaAhyɛnsode}}

Consider the function
. Why do are we required to use a one-sided limit instead of a two-sided limit when investigating the behavior of the function as x approaches 1?

Approaching from the right is just a shortcut to finding the y-intercept.

The function is not defined for x less than 1, so it's impossible to approach 1 from the left.

The left-hand limit would automatically equal infinity, which is too difficult to graph.

Square root functions can only ever be evaluated using right-hand limits.

Asemmisa {{asɛmmisaAhyɛnsode}}

Which of the following is the most mathematically sound practice when using a graph to investigate a limit?

Assume the limit does not exist if the graph requires you to change the default zoom settings.

Treat the graph as a helpful visual hypothesis, but verify the behavior using algebraic properties or numerical tables.

Only look at the graph from a zoomed out perspective where the entire domain is visible at once.

Trust the first visual output you see, as modern graphing software doesn't make mistakes.

🔵 1.1 Limits of Functions Using Numerical and Graphical Techniques | Instruction Day 2 of 2

A student looks at the graph of the piecewise function and notes that and What is the correct conclusion regarding the overall limit , and why?

Consider the function . Why do are we required to use a one-sided limit instead of a two-sided limit when investigating the behavior of the function as x approaches 1?

Which of the following is the most mathematically sound practice when using a graph to investigate a limit?

A student looks at the graph of the piecewise function and notes that and
What is the correct conclusion regarding the overall limit , and why?

Consider the function
. Why do are we required to use a one-sided limit instead of a two-sided limit when investigating the behavior of the function as x approaches 1?