LIMITS
LIMITS
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In mathematics, limits are a fundamental concept used to describe the behavior of functions and sequences as their inputs approach certain values.
A limit determines what value a function or sequence tends to as the input gets arbitrarily close to a particular point.
[ As we can see in the graph, there is a line that passes through the point. That line represents the function, and the point represents the limit of the function. The arrow that we see facing the point indicates that the function is approaching that point.]
LIMITS OF FUNCTION
LIMITS OF FUNCTION
It is read as “the limit of f of x, as x approaches a equals L”. The “lim” shows limit, and fact that function f(x) approaches the limit L as x approaches a is described by the right arrow.
EXAMPLES
EXAMPLES
1. lim (3x) = 24
× → 8
Solution:
To solve the limit of 3x as x approaches 8:
Step 1: Substitute the value 8 into the function:
3(8)
Step 2: Simplify by Multiplying:
3(8) = 24
Step 3: Therefore, the limit of the function 3x as x approaches 8 is 24.
2. lim (x) = 2
x→ 2
In the lim (x) as x approaches 2, the number 2 is a constant.
To solve this limit, we can directly conclude that the limit of
the function x as x approaches 2 is equal to the constant 2.
3. lim (4x-3) = 1
× → 1
Solution:
To solve the limit of 4x-3 as x approaches 1:
Step 1: Substitute the value 1 into the function:
4(1) - 3
Step 2: Simplify the calculation inside the parentheses:
4(1) - 3 = 1
Step 3: Therefore, the limit of the function 4x-3 as x approaches 1 is 1.
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