One convenient way to find the sum of the Maclaurin series is to start with a well-known Maclaurin series and then manipulate it one step at a time until it matches the series you’ve been given. Because you’ll be manipulating the expression of the sum at the same time, once you get the series to match, you’ll automatically have the sum.

Read MoreMultiplying multivariable polynomials (polynomials with two or more different variables) is very similar to multiplying single-variable polynomials (those that have just one variable). You’ll just need to be careful about combining like terms.

Read MoreIn this lesson we’ll look at different types of triangles and how to use Pythagorean inequalities to determine what kind of triangle we have based on their angle measures and side lengths.

Read MoreType I error rate is the rejecting the null hypothesis when it’s true, and Type II error rate is the probability of accepting the null hypothesis when it’s false. Type I error is called “alpha,” and Type II error is called “beta.”

Read MoreTo find the equation of the tangent line using implicit differentiation, follow three steps. First differentiate implicitly, then plug in the point of tangency to find the slope, then put the slope and the tangent point into the point-slope formula.

Read MoreWhen we talk about place value, we’re talking about the value of the location of a particular digit within a given number (the value of the place where that digit is located within that number). Given any decimal number, place value is what allows us to easily say where each digit of the number is located.

Read MoreGiven that the numerator is a constant and the denominator is any function, the derivative will be the negative constant, multiplied by the derivative of the denominator divided by the square of the denominator.

Read MoreTo sketch a polar curve, first find values of r at increments of theta, then plot those points as (r, theta) on polar axes. Then connect the points with a smooth curve to get the full sketch of the polar curve.

Read MoreUniform motion explains the distance of an object when it travels at a constant speed, the rate, over a period of time. To compare different rates, times, and distances you can use subscripts to keep track of which pieces go with which equation.

Read MoreIt’s important to know whether we’re talking about a population or a sample, because in this section we’ll be talking about variance and standard deviation, and we’ll use different formulas for variance and standard deviation depending on whether we’re using data from a population or data from a sample.

Read MoreYou’re usually given a position equation x or s(t), which tells you the object’s distance from some reference point. This equation also accounts for direction, so the distance could be negative, depending on which direction your object moved away from the reference point.

Read MoreIf you need to find the sum of a series, but you don’t have a formula that you can use to do it, you can instead add the first several terms, and then use the integral test to estimate the very small remainder made up by the rest of the infinite series. The sum of the series is usually the sum of the first several terms, plus a very smaller error that you can estimate.

Read MoreMeasures of central tendency are different ways we’ve come up with to describe the “middle,” “center,” or most typical value of the data. They include the mean, the median, and the mode, and we need to know how to find all three.

Read MorePower rule works for differentiating power functions. To use power rule, multiply the variable’s exponent by its coefficient, then subtract 1 from the exponent.

Read MorePopulation systems are always cooperative, competitive, or predator-prey. We’ll talk about how to determine the kind of system we have, and how to solve predator-prey systems for their equilibrium values.

Read MoreFinding derivatives of a multivariable function means we’re going to take the derivative with respect to one variable at a time. For example, we’ll take the derivative with respect to x while we treat y as a constant, then we’ll take another derivative of the original function, this one with respect to y while we treat x as a constant.

Read MoreIf two planes intersect each other, the curve of intersection will always be a line. To find the symmetric equations that represent that intersection line, you’ll need the cross product of the normal vectors of the two planes, as well as a point on the line of intersection.

Read MoreTo avoid confusion between negative exponents and inverse functions, sometimes it’s safer to write arcsin instead of sin^(-1) when you’re talking about the inverse sine function. The same thinking applies to the other five inverse trig functions.

Read MoreWe’ll look at how to add and subtract fractions that have variables in them as well as numbers. We’ll start by finding a common denominator from the factors of each of the individual denominators.

Read MoreTo solve an equation that has parentheses in it, start by simplifying both sides of the equation by distributing any coefficients in front of the parentheses. Then follow order of operations to simplify further and solve for the variable.

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