Section 3.5

Make sure you understand our new notation.

stands for the change in y on the graph of the function.

dy stands for the change in y on the tangent line.

stands for the change in x on the graph of the function.

dx stands for the change in x on the tangent line.

For problems 39-46, finding dy is a two step process. First find , then multiply both sides by dx. To find in problems 39-42, just compute the numerator of the definition of the derivative, without the limit. Instead of h, we use .

For problems 23-31, you must use the formula (1) in the blue box above example 1 in your text. Memorize it! To use thus formula, you must first identify f(x), x₀, and .

f(x) is easy. If you are cubing something, f(x) = x³. If you are taking the sine of something, f(x) = sinx. x₀ is the value of x near the one you are given for which you can easily evaluate the function without a calculator. is the amount the number you are given differs from x₀. If the number you are given is bigger than x₀, then is positive. If the number you are given is smaller than x₀, then is negative. For example, suppose you are asked to estimate (1.98)⁵. f(x) is x⁵, x₀ is 2, and is -0.02.

For the word problems in the homework, if the problem is talking about the error in a side, represent it by s. If it is talking about the percentage error in a side, represent it by .