I have been an educator for the past thirty years. I have taught both calculus and physics for all of those years and currently teach precalculus as well. I have been the math department chair at Hobart for the past ten years. Additionally, I have taught SAT prep courses and dual credit courses through both Purdue University and Ivy Tech. I have tutored previously through WyzAnt.
If $ f(x) = \frac{x^2-x}{x-1} $ and $ g(x) = x $ is it true that $ f = g $?
Sketch the graph of an example of a function $ f $ that satisfies all of the given conditions.
$ \displaystyle \lim_{x \to 3^+}f(x) = 4 $, $ \displaystyle \lim_{x \to 3^-}f(x) = 2 $,$ \displaystyle \lim_{x \to -2}f(x) = 2 $, $ f(3) = 3 $, $ f(-2) = 1 $
(a) Estimate the area under the graph of $ f(x) = \sin x $ from $ x = 0 $ to $ x = \pi/2 $ using four approximating rectangles and right endpoints. Sketch the graph and the rectangles. Is your estimate an underestimate or an overestimate?
(b) Repeat part (a) using left endpoints.
Evaluate the indefinite integral.
$ \displaystyle \int e^x \sqrt{1 + e^x} \, dx $
Suppose you start at the origin, move along the x-axis a distance of 4 units in the positive direction, and then move downward a distance of 3 units. What are the coordinates of your position?
A ream of $20-$ lb paper contains 500 sheets and is about 2 in. high. Suppose you take one sheet, fold it in half, then fold it in half again, continuing in this way as long as possible. Source: The AMATYC Review.After folding 50 times (if this were possible), what would be the height (in miles) of the folded paper?
Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the following methods with n=4. f(x) = -x^2 + 9 from x = -2 to x = 2.(a) Use left endpoints.(b) Use midpoints.
A rectangular piece of tin has an area of 527 square inches. A square of 5 inches is cut from each corner and the sides folded up and soldered together to form an open box with volume 735 cubic inches. Set up a system of equations to model this situation, then solve your system to determine the dimensions of the original rectangle.
You will need a calculator for this one. Estimate the area under the graph of f(x) = sin(2x) from x = 5 to x = 8 using 3 approximating rectangles and left endpoints.
A trough is 12 ft long and its ends have the shape ofisosceles triangles that are 5 ft across at the top andhave a height of 1 ft. If the trough is being filled with water ata rate of 11 ft3/min, how fast is the waterlevel rising when the water is 8 inches deep?
Suppose the cost and revenue functions of a company are R(x) = 60x and C(x) = 360 + 40x + 0.1x² respectively, where x is the number of units produced and sold.a) Find the maximum profit.b) Find the number of units needed to break even.
A particle moves along a horizontal line and its position function is s(t) for t ≥ 0. Find the maximum speed and time when it occurs, the displacement of the particle, and the distance traveled by the particle over the interval.s(t) = t^3 - 10t^2Interval: 1 ≤ t ≤ 12
