Calculating Limits Using the Limit Laws

Front

What is the limit law for the sum of two functions?

Back

If \( \lim_{x \to c} f(x) = L_1 \) and \( \lim_{x \to c} g(x) = L_2 \), then \( \lim_{x \to c} (f(x) + g(x)) = L_1 + L_2 \).

Front

What is the limit law for the difference of two functions?

Back

If \( \lim_{x \to c} f(x) = L_1 \) and \( \lim_{x \to c} g(x) = L_2 \), then \( \lim_{x \to c} (f(x) - g(x)) = L_1 - L_2 \).

Front

What is the limit law for the product of two functions?

Back

If \( \lim_{x \to c} f(x) = L_1 \) and \( \lim_{x \to c} g(x) = L_2 \), then \( \lim_{x \to c} (f(x) \cdot g(x)) = L_1 \cdot L_2 \).

Front

What is the limit law for the quotient of two functions?

Back

If \( \lim_{x \to c} f(x) = L_1 \) and \( \lim_{x \to c} g(x) = L_2 \) and \( L_2 \neq 0 \), then \( \lim_{x \to c} \frac{f(x)}{g(x)} = \frac{L_1}{L_2} \).

Front

What is the limit of a constant function?

Back

If \( f(x) = k \) (a constant), then \( \lim_{x \to c} f(x) = k \).

Front

What is the limit of a polynomial function as x approaches a value?

Back

For a polynomial \( p(x) \), \( \lim_{x \to c} p(x) = p(c) \).

Front

What is the limit of a rational function as x approaches a value?

Back

For a rational function \( \frac{p(x)}{q(x)} \), if \( q(c) \neq 0 \), then \( \lim_{x \to c} \frac{p(x)}{q(x)} = \frac{p(c)}{q(c)} \).

Front

Evaluate \( \lim_{x \to 3} (f(x) + g(x)) \) if \( \lim_{x \to 3} f(x) = 4 \) and \( \lim_{x \to 3} g(x) = 0 \).

Back

The limit is 4.

Front

Evaluate \( \lim_{x \to c} \sqrt{3h(x) - 2g(x)} \) given \( \lim_{x \to c} h(x) = 4 \) and \( \lim_{x \to c} g(x) = -2 \).

Back

The limit is 4.

Front

Evaluate \( \lim_{x \to 3} (f(x) - h(x)) \) if \( \lim_{x \to 3} f(x) = 5 \) and \( \lim_{x \to 3} h(x) = 0 \).

Back

The limit is 5.