IB Math AI Topic 5 Calculus Review

Front

What is the Trapezoidal Rule?

Back

A numerical method to estimate the area under a curve by dividing it into trapezoids.

Front

How do you calculate the limit of a function as x approaches a value?

Back

Evaluate the function at values increasingly close to the target value and determine the value it approaches.

Front

What is the derivative of a function?

Back

The derivative represents the rate of change of a function with respect to its variable.

Front

If f'(x) = 4x, what is f(x)?

Back

f(x) = 2x² + C, where C is a constant.

Front

What is the Fundamental Theorem of Calculus?

Back

It links the concept of differentiation and integration, stating that the integral of a function can be found using its antiderivative.

Front

How do you find the slope of a tangent line to a curve at a point?

Back

Calculate the derivative of the function at that point.

Front

What is a normal line to a curve?

Back

A line that is perpendicular to the tangent line at a given point on the curve.

Front

What is the integral of t^n with respect to t?

Back

(1/(n+1))t^(n+1) + C, where n ≠ -1.

Front

What does 'C' represent in an indefinite integral?

Back

C represents the constant of integration, accounting for all possible vertical shifts of the antiderivative.

Front

How do you estimate the area under a curve using the Trapezoidal Rule?

Back

Divide the area into trapezoids, calculate the area of each, and sum them up.