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No Solution Systems of Equations

"Sometimes we have a system of equations that has either infinite or zero solutions. We call these no solution systems of equations. When we solve a system of equations and arrive at a false statement ...

Basic Transformations

"When graphing polynomials, basic transformations occur when a graph either shifts along the x-axis or y-axis and/or dilates. When graphing transformations, a dilation occurs when the "a" term value i ...

Negative Exponents

"It's important to understand what It means to have negative exponents and zero exponents. Negative exponents put the exponentiated term in the denominator of a fraction and zero exponents just make t ...

Navigation Problems

"The word problems encountered most often with vectors are navigation problems. These navigation problems use variables like speed and direction to form vectors for computation. Some navigation proble ...

Natural Logarithm

"The natural log is the logarithm to the base of the number e and is the inverse function of an exponential function. Natural logarithms are special types of logarithms and are used in solving time an ...

Natural Log Integration

"Because the derivatives of e^x and ln(x) are e^x and 1/x, respectively, the integrals of the latter two functions are just the former. If the variable parts of these functions are not just x, but a p ...

Multiplying Rationals

"Multiplying rational expressions is basically two simplifying problems put together. When multiplying rationals, factor both numerators and denominators and identify equivalents of one to cancel. Div ...

Multiplying Radicals

"When multiplying radical expressions, it is helpful to remember that only terms "inside" the radicals can be multiplied and only the terms "outside" the radical can be multiplied together. After mul ...

Multiplying Radical Expressions

"When multiplying radical expressions of the same power, be careful to multiply together only the terms inside the roots and only the terms outside the roots; keep them separate. After multiplying th ...

Average Value of a Function

"Calculating the average value of a function over a interval requires using the definite integral. The exact calculation is the definite integral divided by the width of the interval. This calculates ...

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