AP Calculus Unit 1

Front

What is a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches some value.

Front

If \( \lim_{x\rightarrow c}f(x)=3 \), \( \lim_{x\rightarrow c}g(x)=-2 \), and \( \lim_{x\rightarrow c}h(x)=4 \), what is \( \lim_{x\rightarrow c}(f(x)+2g(x)-h(x)) \)?

Back

\( -1 \)

Front

What does it mean for a function to be continuous on an interval?

Back

A function is continuous on an interval if there are no breaks, jumps, or holes in the graph of the function on that interval.

Front

TRUE OR FALSE? If f is continuous on [-1,1], f(-1)=4 and f(1)= -2, then there is a zero between -1 and 1.

Back

TRUE

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line \( x = a \) where a function approaches infinity or negative infinity as the input approaches \( a \).

Front

How do you find the vertical asymptote of a rational function?

Back

Set the denominator equal to zero and solve for x.

Front

What is the definition of continuity at a point?

Back

A function f is continuous at a point c if \( \lim_{x \to c} f(x) = f(c) \).

Front

What is the Squeeze Theorem?

Back

If \( f(x) \leq g(x) \leq h(x) \) for all x near c, and \( \lim_{x \to c} f(x) = \lim_{x \to c} h(x) = L \), then \( \lim_{x \to c} g(x) = L \).

Front

What is the difference between one-sided limits and two-sided limits?

Back

One-sided limits approach a value from one side (left or right), while two-sided limits approach from both sides.

Front

What is the limit of a constant function?

Back

The limit of a constant function is the constant itself, regardless of the input.