Question 1
What concept helps in understanding indeterminate forms like \( \frac{0}{0} \) in limits?
Question 2
What is the anti-derivative (indefinite integral) of \( 4x^3 \)?
Question 3
What does the Power Rule for derivatives state?
Question 4
If \( f(x) = x^3 \), what is \( f'(x) \)?
Question 5
What is the process of finding the integral of a function also known as?
Question 6
How do you simplify the limit \( \lim_{{x \to 2}} \frac{x^2 - 4}{x - 2} \)?
Question 7
How do derivatives and integrals compare?
Question 8
What is the slope of the tangent line to the curve \( f(x) = x^3 \) at \( x = 2 \)?
Question 9
How do you find the derivative using the limit process for \( f(x) = x^3 \)?
Question 10
Which formula is used for the slope of a secant line between two points \((x_1, y_1)\) and \((x_2, y_2)\)?
Question 11
For the function \( A(t) = 0.01t^2 + 0.5t + 100 \), what is the rate of change at t = 10?
Question 12
What is the formula for calculating the area under a curve using integration?
Question 13
What does the value of \( \lim_{{x \to 2}} \frac{x^2 - 4}{x - 2} \) evaluate to?
Question 14
If \( \frac{d}{dx}[x^2] = 2x \), what is \( \frac{d}{dx}[2x] \)?
Question 15
What is the integral of the rate function \( R(t) = 0.5t + 20 \) from t = 20 to t = 100?