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f(x)= 3/(x-1)
find the x and y intercepts, vertical and horizontal asymptotes, x coordinates of the critical points, open intervals where the function is concave up and concave down, relative minima and maxima.
Could you also sketch the graph of the function as well.
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a balloon leaves the ground 18m horizontally from an observer and rises vertically at 1.25 m/s.
A. how fast in m/s is the balloon receding from the observer after 8 seconds?
B. when the balloon is 20m vertically above the ground, at what rate is its distance from the observer changing?
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A wire of length 20m is cut into two parys, one of which is bent into a circle and the other into a square. if the sum of the area of the figures is maximum,
a. find the diameter of the circle.
b. find the side of the square.
c. find the sumof the maximum area of the two figures in m^2.
Show that improper integral ∫ x^2/((e^x)-1) is converging.(integral limit 0 to positive infinity)
Determine the domain of the function f(x)=-x-10/-3x^3+5x^2+10x
A computer retailing company specializes in the sale of jump drives to community college students.
The demand function for jump drives is P= X2 +10X +1000
dollars
For the same company the average cost function is given as: c= 22 +36x +100 -2/x
dollars
Where p is the price in dollars and x represents units of output.
i) Determine the revenue function
ii) Determine the cost function
iii) Determine the profit function
iv) Find the price and output that will maximize profit.
v) Find the maximum profit
Suppose you are buying face mask for yourself, your friends, and family during this covid-19
pandemic. The face mask shop has a deal going, if you buy one facemask for 35 pesos, then
additional face masks are only 30 pesos each. Using a short bond paper, do the following:
a. Represent this situation into a rational equation showing the price per face mask based
on the number of face masks.
b. Determine the horizontal asymptote and explain what the horizontal asymptote
represents.
c. Graph the function appropriately and determine its domain and range.
d. Is the original function one-to-one? Explain
Use the Chain Rule to determine an equation for the acceleration when 𝑎 = 𝑑𝑣/ 𝑑𝑡
When 𝑣 = (2𝑡2 + 3)4
and
When 𝑣 = ln(4𝑡3 − 1)
The gain of an amplifier is found to be 𝐺 = 20 ln(𝑉𝑜𝑢𝑡). The tasks are to find equations for: a) Draw a graph of Gain against Vout between 𝑉𝑜𝑢𝑡 = 1 and 𝑉𝑜𝑢𝑡 = 10 b) Determine the gradient of the graph at 𝑉𝑜𝑢𝑡 = 2 and 𝑉𝑜𝑢𝑡 = 5 c) Find the derivative 𝑑𝐺/ 𝑑𝑉𝑂𝑢𝑡 and calculate its value at 𝑉𝑜𝑢𝑡 = 2 and 𝑉𝑜𝑢𝑡 = 5 d) Compare your answers for part b) and part c) e) Find the second derivative 𝑑2𝐺/ 𝑑𝑉𝑂𝑢𝑡 2
Given the function f(x)=x^1/3 + x sqrt x - 1, find formulas to
(a) compress the graph horizontally by a factor of 2 followed by a reflection across the y-axis.
(b) Stress the graph vertically by a factor of 1.5 followed by a reflection across the y-axis.
Write a Mathematica code to display the functions in (a) and (b). Your Mathematica code should produce the graph as displayed in Fig. I(a) and I (b), where the blue, red and brown curves refer to the function f(x),g1(x),g2(x) respectively. g2(x) is the final function while g1(x) is the intermediate function.
#339914 on Dec 2023