8.2 Day 2: Identifying Indeterminate Forms Photo by Vickie Kelly, 2008 Greg Kelly, Hanford High School, Richland, Washington Brooklyn Bridge, New York City What makes an expression indeterminate? Consider: We can hold one part of the expression constant:

ByPhoto by Vickie Kelly, 1998. Greg Kelly, Hanford High School, Richland, Washington. Trapezoidal Rule. Mt. Shasta, California. Using integrals to find area works extremely well as long as we can find the antiderivative of the function.

ByPhoto by Vickie Kelly, 2002. Greg Kelly, Hanford High School, Richland, Washington. 5.1 Estimating with Finite Sums. Greenfield Village, Michigan. velocity. time. Consider an object moving at a constant rate of 3 ft/sec. Since rate . time = distance:.

ByPhoto by Vickie Kelly, 2006. Greg Kelly, Hanford High School, Richland, Washington. 2.2 Limits Involving Infinity. North Dakota Sunset. As the denominator gets larger, the value of the fraction gets smaller. There is a horizontal asymptote if:. or.

ByPhoto by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. 3.2 Differentiability. Arches National Park. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. Arches National Park.

By2.3 Continuity. Photo by Vickie Kelly, 2002. Greg Kelly, Hanford High School, Richland, Washington. Grand Canyon, Arizona. 2. 1. 1. 2. 3. 4.

ByPhoto by Vickie Kelly, 1998. Greg Kelly, Hanford High School, Richland, Washington. 5.5 Numerical Integration. Mt. Shasta, California. Using integrals to find area works extremely well as long as we can find the antiderivative of the function.

By6.4 Exponential Growth and Decay. Glacier National Park, Montana Photo by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington.

By7.1 Integral as Net Change. Photo by Vickie Kelly, 2006. Greg Kelly, Hanford High School, Richland, Washington. A honey bee makes several trips from the hive to a flower garden. . The velocity graph is shown below. What is the total distance traveled by the bee?. 700 feet. 200ft. 200ft.

ByPhoto by Vickie Kelly, 2006. Greg Kelly, Hanford High School, Richland, Washington. 7.3 day 3. The Shell Method. Grows to over 12 feet wide and lives 100 years. Japanese Spider Crab Georgia Aquarium, Atlanta.

ByPhoto by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington. Mt. Rushmore, South Dakota. 3.9: Derivatives of Exponential and Logarithmic Functions. Look at the graph of . If we assume this to be true, then:. The slope at x=0 appears to be 1. definition of derivative.

ByPhoto by Vickie Kelly, 1993. Greg Kelly, Hanford High School, Richland, Washington. 2.4 Rates of Change and Tangent Lines. Devil’s Tower, Wyoming. The slope of a line is given by:. The slope at (1,1) can be approximated by the slope of the secant through (4,16).

By10.2 day 1: Vectors in the Plane. Mesa Verde National Park, Colorado. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. Warning: Only some of this is review . Quantities that we measure that have magnitude but not direction are called scalars .

ByPhoto by Vickie Kelly, 1999. Greg Kelly, Hanford High School, Richland, Washington. 7.4 Day 1 Lengths of Curves. Golden Spike National Historic Site, Promontory, Utah. Length of Curve (Cartesian). Lengths of Curves:.

ByPhoto by Vickie Kelly, 1998. Greg Kelly, Hanford High School, Richland, Washington. 5.5 Numerical Integration. Mt. Shasta, California. Using integrals to find area works extremely well as long as we can find the antiderivative of the function.

By9.2 day 2. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. Finding Common Maclaurin Series. Liberty Bell, Philadelphia, PA. Maclaurin Series:. (generated by f at ).

ByPhoto by Vickie Kelly, 2008. Greg Kelly, Hanford High School, Richland, Washington. 10.1 Parametric functions. Mark Twain’s Boyhood Home Hannibal, Missouri. Photo by Vickie Kelly, 2008. Greg Kelly, Hanford High School, Richland, Washington. Mark Twain’s Home Hartford, Connecticut.

By8.2 Day 2: Identifying Indeterminate Forms. Photo by Vickie Kelly, 2008. Greg Kelly, Hanford High School, Richland, Washington. Brooklyn Bridge, New York City. What makes an expression indeterminate?. Consider:. We can hold one part of the expression constant:.

ByPhoto by Vickie Kelly, 1999. Greg Kelly, Hanford High School, Richland, Washington. 4.4 Modeling and Optimization. Buffalo Bill’s Ranch, North Platte, Nebraska. There must be a local maximum here, since the endpoints are minimums. A Classic Problem.

By8.4 day 2 Tests for Convergence. Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2006. Riverfront Park, Spokane, WA. If then gets bigger and bigger as , therefore the integral diverges .

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