Gr12 Mathematics: Ch 5.1 Limits

What is the fundamental concept that calculus is built on?

Algebra

Limits (correct)

Optimization

Geometry

Who is known for his paradoxes, including the Achilles and the Tortoise Paradox?

Zeno of southern Italy (correct)

Achilles

Archimedes

Euclid

What is the value of x that makes the function y = (x^2 + 4x - 12)/(x + 6) undefined?

x = -2

x = -4

x = -6 (correct)

x = 0

What is the value of the limit as x approaches -6 for the function y = (x^2 + 4x - 12)/(x + 6)?

-8 Signup and view all the answers

What is the graphical representation of the function y = (x^2 + 4x - 12)/(x + 6)?

A straight line with a hole at x = -6 Signup and view all the answers

What notation is used to represent the limit as x approaches -6 for the function y = (x^2 + 4x - 12)/(x + 6)?

lim x→-6 ((x + 6)(x - 2))/(x + 6) = -8 Signup and view all the answers

What is the purpose of differential calculus in optimization problems?

All of the above Signup and view all the answers

What are the two branches of calculus?

Differential calculus and Integral calculus Signup and view all the answers

What is the importance of the concept of limits in calculus?

It allows us to study how functions behave as the input values approach a specific point Signup and view all the answers

What happens to the function y = (x^2 + 4x - 12)/(x + 6) when x = -6?

The function becomes undefined Signup and view all the answers

What is the significance of the Achilles and the Tortoise Paradox?

It illustrates the concept of limits Signup and view all the answers

What can be inferred about the function y = x - 2?

It is a linear function with no holes or zeros Signup and view all the answers

What is the purpose of canceling out the (x + 6) terms in the function y = ((x + 6)(x - 2))/(x + 6)?

To simplify the function Signup and view all the answers

What is the graphical representation of the function y = ((x + 6)(x - 2))/(x + 6)?

A straight line with a hole at x = -6 Signup and view all the answers

What is the value of y when x is close to -6 for the function y = ((x + 6)(x - 2))/(x + 6)?

y approaches -8 Signup and view all the answers

What is the notation used to represent the limit of the function y = ((x + 6)(x - 2))/(x + 6) as x approaches -6?

lim (x → -6) ((x + 6)(x - 2))/(x + 6) Signup and view all the answers

What is the primary concept underlying the Achilles and the Tortoise Paradox?

Limits Signup and view all the answers

What happens to the function y = (x^2 + 4x - 12)/(x + 6) when we cancel out the (x + 6) terms?

The function becomes a straight line without a hole Signup and view all the answers

What can be inferred about the graph of the function y = (x^2 + 4x - 12)/(x + 6)?

It is a straight line without a hole at x = -6 Signup and view all the answers

What is the significance of the limit concept in differential calculus?

It is used to study the behavior of functions as the input approaches a certain value Signup and view all the answers

What is the purpose of the notation lim x → -6 [(x^2 + 4x - 12)/(x + 6)]?

To represent the value of the function as x approaches -6 Signup and view all the answers

What is the relationship between the function y = (x^2 + 4x - 12)/(x + 6) and the function y = x - 2?

They are equivalent functions except at x = -6 Signup and view all the answers

What is the primary application of differential calculus?

Solving optimization problems Signup and view all the answers

What is the fundamental branch of mathematics that differential calculus is a part of?

Calculus Signup and view all the answers