Limit Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Find lim⁡x→3(2x+1)\lim_{x \to 3} (2x + 1)

Solution

  1. 1
    Since 2x+12x + 1 is a polynomial, it is continuous everywhere.
  2. 2
    For continuous functions, we can evaluate the limit by direct substitution.
  3. 3
    Substitute x=3x = 3: 2(3)+1=6+1=72(3) + 1 = 6 + 1 = 7.

Answer

lim⁡x→3(2x+1)=7\lim_{x \to 3} (2x + 1) = 7
When a function is continuous at a point, the limit equals the function value at that point. Polynomials are continuous everywhere, so direct substitution always works for polynomial limits.

About Limit

The value a function gets closer and closer to as the input approaches a specific target value, without necessarily reaching it.

Learn more about Limit →

More Limit Examples

Example 2 medium

Find [formula]

Example 3 hard

Find [formula]

Example 4 easy

Find [formula]

Example 5 medium

Find [formula]

← All Limit Examples Limit Concept