Front

What is the definition of convergence in the context of infinite series?

Back

A series converges if the sum of its terms approaches a finite limit as the number of terms increases.

Front

What is the definition of divergence in the context of infinite series?

Back

A series diverges if the sum of its terms does not approach a finite limit as the number of terms increases.

Front

What is implicit differentiation?

Back

Implicit differentiation is a technique used to find the derivative of a function defined implicitly by an equation involving both x and y.

Front

What is the formula for the trapezoidal rule?

Back

The trapezoidal rule estimates the area under a curve by dividing it into trapezoids and summing their areas: A ≈ (b-a)/2 * (f(a) + f(b)).

Front

What is the process of separation of variables in differential equations?

Back

Separation of variables is a method for solving differential equations by rearranging the equation to isolate the variables on opposite sides.

Front

What is the significance of the constant of integration in indefinite integrals?

Back

The constant of integration represents the family of all antiderivatives of a function, as indefinite integrals can differ by a constant.

Front

How do you find dy/dx using implicit differentiation for the equation x^3 + y^3 = 36?

Back

Differentiate both sides with respect to x, applying the chain rule to y, and solve for dy/dx to get dy/dx = -x^2/y^2.

Front

What is a trapezoidal sum?

Back

A trapezoidal sum is an approximation of the integral of a function using trapezoids to estimate the area under the curve.

Front

What is the first step in evaluating an indefinite integral?

Back

The first step is to identify the function to be integrated and determine the appropriate integration technique.

Front

What is the relationship between a function and its derivative?

Back

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

Tags

CCSS.HSF.IF.B.4