Introduction:
In general, the limit is an extension up to which something can go. In mathematics, a limit is an intended height of a function. In other words, a limit is defined as the boundary of a specific area. The function limit is most often used in calculus problems.
Generally it is written as
`lim_(x->c)` f (x) = K
Where c - real number (when f(x) is a real valid function).
Properties:
Let the given function be f(x) and x approaches to h.
State all the possibilities.
Simplify the given function to apply the limits and solve.
Replace x for h.
Simplify the function.
The limits of a function could be obtained.
Example problems:
Problem 1: Find the limit of the function f (x) = 3x as x approaches 6.
Solution: Given f (x) = 3x
Substituting the value of x the equation becomes
f (6) = 3 (6) = 18.
So, the limit of f (x) = 3x as x approaches 6 is 18.
Problem 2: Find the limit of the function 9x^2 + 2x – 5 as x approaches 2.
Solution:
Given 9x^2 + 2x – 5
Substituting the values of x
= (9) (2)2 + 2 (2) – 5
= (36 + 4 – 5)
= 35
Hence the limit of 9x^2 + 2x – 5 as x approaches 2 is 35.
Problem 3: Solve (|x^2 - 5x + 6| / (x – 2)) for x approaching to 1
Solution:
Given (|x^2 - 5x + 6| / (x – 2))
Factorize the numerator |x^2 - 5x + 6|
x^2 - 5x + 6 = 0
(x – 2) (x – 3) = 0
The roots are x = 2 and x = 3.
Substitute the roots in the given function
((x – 2) (x – 3) / (x – 2))
Applying the limit
= ((1 - 2) (1 – 3) / (1 – 2))
= (-1) (-2) / (-1)
= 2 / (-1)
= -2
Hence the solution of (|x^2 - 5x + 6| / (x – 2)) is -2
Understanding Derivative Functions is always challenging for me but thanks to all math help websites to help me out.
Practice Problems:
Determine the limit of the function f(y) = -2y as y approaches to 0.5
Answer: -1
Find the limit of f(x) = sin x as x approaches to 0
Answer: 0
Find the limit: f(x) = x^2 - 5x + 6 when x tends to 2
Answer: 0
Solve the following: `lim_(x->3)` (x^2 + 8x + 3) / (x3 + 2x + 1)
Answer: 18 / 17
In general, the limit is an extension up to which something can go. In mathematics, a limit is an intended height of a function. In other words, a limit is defined as the boundary of a specific area. The function limit is most often used in calculus problems.
Generally it is written as
`lim_(x->c)` f (x) = K
Where c - real number (when f(x) is a real valid function).
Properties:
Let the given function be f(x) and x approaches to h.
State all the possibilities.
Simplify the given function to apply the limits and solve.
Replace x for h.
Simplify the function.
The limits of a function could be obtained.
Example problems:
Problem 1: Find the limit of the function f (x) = 3x as x approaches 6.
Solution: Given f (x) = 3x
Substituting the value of x the equation becomes
f (6) = 3 (6) = 18.
So, the limit of f (x) = 3x as x approaches 6 is 18.
Problem 2: Find the limit of the function 9x^2 + 2x – 5 as x approaches 2.
Solution:
Given 9x^2 + 2x – 5
Substituting the values of x
= (9) (2)2 + 2 (2) – 5
= (36 + 4 – 5)
= 35
Hence the limit of 9x^2 + 2x – 5 as x approaches 2 is 35.
Problem 3: Solve (|x^2 - 5x + 6| / (x – 2)) for x approaching to 1
Solution:
Given (|x^2 - 5x + 6| / (x – 2))
Factorize the numerator |x^2 - 5x + 6|
x^2 - 5x + 6 = 0
(x – 2) (x – 3) = 0
The roots are x = 2 and x = 3.
Substitute the roots in the given function
((x – 2) (x – 3) / (x – 2))
Applying the limit
= ((1 - 2) (1 – 3) / (1 – 2))
= (-1) (-2) / (-1)
= 2 / (-1)
= -2
Hence the solution of (|x^2 - 5x + 6| / (x – 2)) is -2
Understanding Derivative Functions is always challenging for me but thanks to all math help websites to help me out.
Practice Problems:
Determine the limit of the function f(y) = -2y as y approaches to 0.5
Answer: -1
Find the limit of f(x) = sin x as x approaches to 0
Answer: 0
Find the limit: f(x) = x^2 - 5x + 6 when x tends to 2
Answer: 0
Solve the following: `lim_(x->3)` (x^2 + 8x + 3) / (x3 + 2x + 1)
Answer: 18 / 17
