Techniques for Computing Limits 2.3 Calculus 1

The limit of a constant IS the constant. No matter what “x” approaches Limit Laws

The limit of a sum is the sum of the limits. Theorem 2.3 (1)

The limit of a difference is the difference of the limits. Theorem 2.3 (2)

The limit of a constant times a function is the constant times the limit of the function. Theorem 2.3 (3)

The limit of a product is the product of the limits. Theorem 2.3 (4)

The limit of a quotient is the quotient of the limits. Theorem 2.3 (5)

Theorem 2.3 (6) The limit of a “function raised to a power” is the “limit of the function” raised to the power.

Theorem 2.3 (7) The limit of a “function raised to a fractional power” is the “limit of the function” raised to the fractional power.

Factor and simplify Other Techniques

Sometimes when you have radicals you need to multiply by the conjugate of the numerator or denominator.

Squeeze Theorem Pinching Theorem Sandwich Theorem

Piecewise If x < -1 If x ≥ -1