Question 1
Identify the first step in solving a limit problem using factoring?
Question 2
Which rule applies to the derivative of \( f(x)g(x) \)?
Question 3
Which test is used to identify maxima or minima of a function?
Question 4
When should you use u-substitution in integration?
Question 5
What is the derivative of \( f(x) = (2x^5 + 3x)^2 \) using the chain rule?
Question 6
How do you ensure that a piecewise function is continuous at a boundary point?
Question 7
Which method would you use to evaluate the limit \( \lim_{{x \to 3}} \frac{{x^2 - 9}}{{x - 3}} \)?
Question 8
What is the second derivative used for in calculus?
Question 9
What is the average value of a function \( f(x) \) over \([a, b]\)?
Question 10
What is the integral of \( f(x) = 4x^5 \)?
Question 11
When using related rates, how should you differentiate relations with respect to time?
Question 12
What is the formula for the derivative of a function multiplied by a constant (\( cf(x) \))?
Question 13
What is the derivative of \( ln(x) \)?
Question 14
How do you find the derivative of \( y = e^{3x} \)?
Question 15
What technique is used to find the slope of a tangent line to an implicit curve?