what are the 8 theorems on limits of a function?

Answer 1

The eight key theorems on limits of a function are:

1. Limit of a Sum: The limit of the sum of two functions is the sum of their limits.
2. Limit of a Difference: The limit of the difference of two functions is the difference of their limits.
3. Limit of a Product: The limit of the product of two functions is the product of their limits.
4. Limit of a Quotient: The limit of the quotient of two functions is the quotient of their limits, provided the limit of the denominator is not zero.
5. Limit of a Constant Multiple: The limit of a constant multiplied by a function is the constant multiplied by the limit of the function.
6. Limit of a Composite Function (Continuous): If ( f ) is continuous at ( c ) and ( \lim_{x \to a} g(x) = c ), then ( \lim_{x \to a} f(g(x)) = f(c) ).
7. Squeeze Theorem: If ( f(x) \leq g(x) \leq h(x) ) for all ( x ) near ( a ), and ( \lim_{x \to a} f(x) = \lim_{x \to a} h(x) = L ), then ( \lim_{x \to a} g(x) = L ).
8. Limits at Infinity: The limit of a function as ( x ) approaches infinity or negative infinity can be evaluated using these properties, often resulting in horizontal asymptotes.