Math 260 Week 1 Lab
Part I: Limits – The limit of a function is a way to see the value that the function approaches as a variable in that function gets close to but not necessarily equal to some other value The four ways we have looked at to find the limit of a function are:
- direct substitution of the limiting number into the function
- simplifying the function first then substitute (factor or rationalize)
- examine values of the function from the left and right of the limiting number
- examine the graph of the function at the limiting value
Part II: (a) Piecewise functions (b) discontinuities
Math 260 Week 2 Lab
Part 1: As we have seen, using lim┬(h→0)〖(f(x+h)-f(x))/h〗 to find a derivative each time is a long process and often cumbersome. But, there are a few algorithms that work perfectly for finding derivatives. They are the power rule, the product rule, the quotient rule, and the chain rule.
Part 2: Higher Order Derivatives
Math 260 Week 3 Lab
– In calculus, much effort is devoted to determining the behavior of the graph of a function over an interval on the Cartesian Plane. Finding x & y intercepts, asymptotes, intervals of increasing or decreasing, local maximum and local minimum points, concavity/curvature can all be done using Algebra and Calculus.
– Tangent and Normal lines
Math 260 Week 4 Lab
Part I: The Trig Derivatives – Although the derivative of each trig function can …. found by using trig identities and the formula lim┬(h→0)〖(f(x+h)-f(x))/h〗 , it is far simpler to memorize them because they will be used in many of the techniques that follow in this class as well as in Calculus II.
Part II: Inverse Trigonometric Functions: arcsine or sin-1(u) and arccosine or cos-1(u)
Math 260 Week 5 Lab
- Category 1: Derivatives of Exponentials: eu
- Category-2: Derivatives of Logarithms
- Category 3: L’Hopital’s Rule:
- Part II: Use your Calculator to determine the following:
Math 260 Week 6 Lab
Antiderivatives – According to the first part of the fundamental theorem of calculus, the antiderivative reverses the derivative. If f(x) is a derivative, F(x) is the antiderivative.
Part II: Finding the Area Under a Curve – The area under a curve can …. found by filling the area with rectangles, then finding the area of each rectangle, then adding the areas together. To find an approximate area under a curve, find the total area for both left and right rectangles, then average the two. These are ….. Riemann sums and are the basis of the integral.
Math 260 Week 7 Lab
- Logarithmic Integrals – Examine each example below then answer questions 1–3.
- Exponential Integrals – Examine each example below and answer questions 7–10.
- Bandwidth of a Series Resonance Circuit – The area under the curve shows all acceptable signals with frequency greater than f L and less than f H that can pass through the resonance circuit. This is used in radio receivers to tune for different channels.
- Secant and Cosecant, Tangent and Cotangent – Examine each example below and answer the following questions.