I have been teaching mathematics and computers at East Allegheny Jr/Sr High School for 28 years. I am currently the math department head and was a National Board Certified Teacher (AYA Mathematics) from 2008 - 2018. I co-sponsor East Allegheny's STEM Club and Robotics team. I strongly believe that all children deserve a quality education regardless of their zip code.
Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval.
$ f(x) = x + \sqrt{x - 4}, \hspace{5mm} [4, \infty) $
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.
$ x^4 + x - 3 = 0 $, $ (1, 2) $
Differentiate the function.$ D(t) = \frac {1 + 16t^2}{(4t)^3} $
Find an equation of the tangent line to the curve at the given point.$ y = 2e^x + x, (0,2) $
Explain why the natural logarithmic function $ y = \ln x $ is used much more frequently in calculus that the other logarithmic functions $ y = \log_b x. $
Carbon $ 14 $ dating assumes that the carbon dioxide on Earth today has the same radioactive content as it did centuries ago. If this is true,the amount of $ ^{14} C $ absorbed by a tree that grew several centuries ago should be the same as the amount of $ ^{14} C $ absorbed by a tree growing today. A piece of ancient charcoal contains only $ 15\% $ as much radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal if the half-life of $ ^{14} C $ is $ 5715 $ years?
f(x)=x^3 - 11x^2 +55x - 125a) how many zeros does f(x) haveb) According to Descartes rule of signs, how many positive zerosand negative zeros are there? Show your workc) What are all potential rational zerosd) Find real and complex zeros, if they existe) Show f(x) in factored form
Describe the relationship between right triangles, circles, and trigonometric functions
A company that makes thing-a-ma-bobs has a start-up cost of$34404. It costs the company $1.58 to make each thing-a-ma-bob. Thecompany charges $4.44 for each thing-a-ma-bob.Let x denote the number of thing-a-ma-bobsproduced.Write the cost function for this company.C(x) =Write the revenue function for this company.R(x) =What is the minimum number of thing-a-ma-bobs that the companymust produce and sell to make a profit?
Assume f is the function defined on the interval [-2,-1] by the formula f(x) = 4x^2. Thus the domain of f is the interval [-2,-1], the range of f is the interval [1,4], and the graph of f is shown in part (a).The graph of g is obtained by shifting the graph of f up 4 units.(b) Find the domain of g.Enter your answer in interval notation.D(g) = (c) Give a formula for g in terms of x.g(x) = (d) Find the range of g.Enter your answer in interval notation.R(g) =
A colony of bacteria is growing exponentially, doubling in sizeevery 140 minutes. How many minutes will it take for the colony ofbacteria to become 5 times its current size?
The city of Anville is currently home to 22,000 people, and the population has been growing at a continuous rate of 4% per year. The city of Brinker is currently home to 1,000 people, and the population has been growing at a continuous rate of 5% per year. In how many years will the populations of the two towns be equal? Give your answer accurate to at least 2 decimal places.
