Limits And Continuity

Question 1

What is the course title for MTH 102?

Answer 1

Elementary Mathematics

Question 2

What is the total number of units for the course MTH 102?

Answer 2

3

Question 3

Who is the lecturer for the MTH 102 course?

Answer 3

Dr. Zuonaki Ongodiebi

Question 4

What are the lecture periods for MTH 102?

Answer 4

Monday 3-5 PM; Tuesday 9-12 Noon

Question 5

What is a limit at infinity?

Answer 5

A symbol used to represent a very large number.

Question 6

What is the definition of a one-sided limit?

Answer 6

The limit of a function as it approaches a point from one side (right or left).

Question 7

What does LHS and RHS stand for in the context of limits?

Answer 7

LHS: Left Hand Side, RHS: Right Hand Side

Question 8

What is L’Hôpital’s Rule used for?

Answer 8

To solve problems involving limits that result in indeterminate forms.

Question 9

What are the three conditions for a function f(x) to be continuous at a point?

Answer 9

• f(x) is defined
• Limit of f(x) exists
• Limit of f(x) equals f(x)

Question 10

True or False: A function is discontinuous if any of the three conditions for continuity are not satisfied.

Answer 10

True

Question 11

What does it mean if the limit of a function f exists?

Answer 11

Both the left hand limit and right hand limit exist and are equal.

Question 12

Fill in the blank: A function is discontinuous if it is ______ at a point.

Answer 12

undefined

Question 13

What is the mathematical notation for the limit of a function as x approaches a?

Answer 13

lim (x -> a) f(x)

Question 14

What theorem states that if c is a constant, then limits can be evaluated accordingly?

Answer 14

Theorems on Limits

Question 15

What is the outcome if both the numerator and denominator approach 0 in a limit?

Answer 15

Use L’Hôpital’s Rule or factorization.

Question 16

How can you find points of discontinuity in a function?

Answer 16

Identify where the function is undefined or does not meet continuity criteria.

Question 17

What is the significance of the (+) sign in a one-sided limit notation?

Answer 17

It indicates the limit is approached from the right side.

Question 18

What is the result if a function is continuous at a point?

Answer 18

The function is defined, the limit exists, and the limit equals the function value.

Question 19

List the applications of derivatives mentioned.

Answer 19

• Relative minima and maxima
• Coordinate geometry
• Mechanics

Question 20

What is the purpose of integration in calculus?

Answer 20

To find the anti-derivative or inverse of differentiation.

Question 21

What is the application of integration mentioned in the outline?

Answer 21

• Area under a curve
• Volume of solid of revolution
• Mechanics