BC Calculus AP Exam 1b 2024

Front

What is Euler's method used for?

Back

Euler's method is a numerical technique for approximating solutions to ordinary differential equations (ODEs) using tangent line approximations.

Front

Define the derivative in the context of calculus.

Back

The derivative of a function at a point measures the rate at which the function's value changes as its input changes, representing the slope of the tangent line to the function's graph at that point.

Front

What is an indefinite integral?

Back

An indefinite integral represents a family of functions whose derivative is the integrand, typically expressed with a constant of integration (C).

Front

What is the formula for finding the horizontal asymptote of a rational function?

Back

For a rational function \( f(x) = \frac{P(x)}{Q(x)} \), the horizontal asymptote can be found by comparing the degrees of the polynomials P and Q.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points \( x_1 \) and \( x_2 \) in that interval, if \( x_1 < x_2 \), then \( f(x_1) < f(x_2) \).

Front

What is the significance of the initial condition in solving differential equations?

Back

The initial condition provides a specific value for the function at a given point, allowing for the determination of the particular solution to the differential equation.

Front

Explain the concept of related rates in calculus.

Back

Related rates involve finding the rate at which one quantity changes in relation to another, often using implicit differentiation.

Front

What is the relationship between the derivative and the slope of a curve?

Back

The derivative of a function at a point gives the slope of the tangent line to the curve at that point, indicating the instantaneous rate of change.

Front

How do you determine the critical points of a function?

Back

Critical points occur where the derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection.

Front

What is the purpose of finding the area under a curve using integration?

Back

Finding the area under a curve using integration allows us to calculate total quantities, such as distance, area, or volume, represented by the function.