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Suppose that f(x) is a differentiable function and assume that g(x) is the inverse function of f(x). Let L1(x) be the linearization of f(x) at x=a and let L2(x) be the linearization of g(x) at x=b where b=f(a).
a) Write the formulas for L1(x) and L2(x).
b) How are the slopes of L1(x) and L2(x) related?
c) If the graph of L1(x) is not a horizontal line, then show that L2(x) is the inverse funciton of L1(x)
d) if f'(a) ≠ 1, -1 , explain why the graphs of L1(x) and L2(x) intersect on the line given by y=x
Solve the system using elementary row operations on the equations of the augmented matrix. Follow the systematic elimination proceedure.
where cosh(x)=(e^x+e^-x)/2 is the hyperbolic cosine, which is an important function in physics and engineering.
a metal storage tank with a maximum value of 1200 m^3, is to be constructed in the shape of a right circular cylinder surmounted by a hemisphere. What radial and height dimensions will require the least amount of material?
the base of a solid is an ellipse whose major axis and minor axis are 12 and 8cm long, respectively. what is the volume of the solid if every section perpendicular to the major axis is an is an equilateral triangle.
A group of friends decided to rent a vacation home for a week. They each paid $70 towards the rent. If three more friends had joined them, the cost per person would have been reduced by $14. How many friends went on the trip?
application of differentiation and integration on real world problem.during the summer the temperature inside a van
teri collects loose change in 3 cans placed near cash registers at the mall. one can hold 37.18. the second one can
The current in a circuit is i = 2.00 cos 100t. Find the voltage across a 100-microfarad(uF) capacitor after 0.200 s, if the initial voltage is Zero (one microfarad(uF)=10 to the power of -6 F).
If the sample size is 100, construct a 95% confidence interval estimate of the population proportion of individuals who trust business to "do what is right."
Two tracking stations are on the equator 119 miles apart. A weather balloon is located on a bearing of N 35°E from the western station and a bearing of N 22°E from the eastern station. How far, to the nearest mile, is the balloon from the western ..
A plane flying horizontally at an altitude of 2 mi and a speed of 520 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station. (Round your ans..
The demand function for a certain make of ink-jet cartridge is the following where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand.
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