LIMIT OF TRANSCENDENTAL FUNCTIONS

Limit of Transcendental Functions

Presentation by Group 4

Table of Contents

1. Overview of the Lesson

2. Different Transcendental Functions

3. Limit of Exponential Functions

4. Limit of Logarithmic Functions

5. Limit of Trigonometric Functions

6. Group Members

7. Thanks

Overviewof the Lesson

Limit of Transcendental Functions

Limit of Transcendental Functions

The Limit of transcendental functions can be defined as a function that is not algebraic and cannot be expressed in terms of a finite sequence of algebraic operations such as sine x.

The limit of transcendental functions consists of three topics, and these are trigonometric, exponential, and last logarithmic.

Different Transcendental Functions

Limit of Transcendental Functions

Limit of Exponential Functions

The ThreeTranscendental Functions

Limit of Logarithmic Functions

Limit of Trigonometric Functions

Limit of Exponential Functions

Limit of Transcendental Functions

C = lim fx = f c x -> c b > 0 b ≠ 1 lim b(x) = bc x -> c

Limit of Exponential Functions

Problem #1

Evaluate the function lim 11x+2 x -> 1

Problem #1

Evaluate the function lim 11x+2 x -> 1

Solution:

lim 11x+2 = 111+2 x -> 1 = 113 = 1,331

Therefore, the limit of 11x+2 as x approaches 1 is 1,331

Problem #2

Evaluate the function lim 3x-(-3) x -> 1

Problem #2

Evaluate the function lim 3x-(-3) x -> 1

Solution:

lim 3x-(-3) = 31-(-3) x -> 1 = 31+3 = 34 = 81

Therefore, the limit of 3x-(-3) as x approaches 1 is 81

Problem #3

Evaluate the function lim (5)(2)x-1 x -> 4

Problem #3

Evaluate the function lim (5)(2)x-1 x -> 4

Solution:

lim (5)(2)x-1 = (5)(2)4-1 x -> 4 = (5)(2)3 = (5)(8) = 40

Therefore, the limit of (5)(2)x-1 as x approaches 4 is 40

Limit of Logarithmic Functions

Limit of Transcendental Functions

There are two fundamental properties of limits to find the limits of logarithmic functions and these standard results are used as formulas in calculus for dealing with the functions in which logarithmic functions are involved.

Problem #1

Evaluate the function lim log(x-1) x -> 1

Solve for the Limit

Solution:

Problem #1

lim log(x) = log(1-1) x -> 1 = log(0) = DNE

Evaluate the function lim log(x-1) x -> 1

Therefore, the limit of log(x-1) as x approaches 1 does not exist.

Problem #2

Evaluate the function lim ln(x-1) x -> 1

Solve for the Limit

Solution:

Problem #2

lim ln(x-1) = ln(1-1) x -> 1 = ln(0) = -1

Evaluate the function lim ln(x-1) x -> 1

Therefore, the limit of ln(x-1) as x approaches 1 is -1

Limit of Trigonometric Functions

Limit of Transcendental Functions

Trigonometric functions are the periodic functions that denote the relationship between the angle and sides of a right-angled triangle.

Problem #1

Evaluate the function lim cosx x -> 0

Problem #1

Evaluate the function lim cosx x -> 0

Solution:

lim cosx = cos(0) x -> 0 = 1

Therefore, the limit of cosx as x approaches 0 is 1

Problem #1

Group Members

Charmaine

Francine

Bianca

Lyka

Vincent

Thanks!