Quiz for:
Understanding Limits in Calculus

Question 1

When estimating limits with tables, which x-values should you use?

Question 2

What is the limit \( \lim_{{x \to -2}} \left( -7x^2 + 13x - 25 \right) \)?

Question 3

For the rational function \( f(x) = \frac{(x-1)(x-3)}{(x-2)(x-4)} \), what happens at \( x = 1 \)?

Question 4

Which of the following is a property of limits for a constant k?

Question 5

How does theorem 2.8 help in finding limits involving radicals?

Question 6

In rational functions, if the denominator is non-zero at x = c, what can be said about the limit?

Question 7

What is \( f(5) \) for the function \( f(x) = \sqrt{24 + x^2} \)?

Question 8

What happens to the limit \( \lim_{{x \to 3}} \frac{(x-1)(x-3)}{(x-2)(x-4)} \)?

Question 9

How do properties of limit help in calculations?

Question 10

Which theorem allows you to say \( \lim_{{x \to c}} f(x) = f(c) \) for polynomial functions?

Question 11

For the function \( f(x) = -7x^2 + 13x - 25 \), what is \( f(-2) \)?

Question 12

For a limit not existing due to division by zero, which condition is highlighted?

Question 13

What is the implication if a rational function's denominator equals zero at a point?

Question 14

What does the notation \( \lim_{{x \to c}} f(x) = L \) represent in calculus?

Question 15

Why don't limits always match function values at a point?