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- Calculus volume 1
- Applications of integration
- Calculus of the hyperbolic
Key concepts
- Hyperbolic functions are defined in terms of exponential functions.
- Term-by-term differentiation yields differentiation formulas for the hyperbolic functions. These differentiation formulas give rise, in turn, to integration formulas.
- With appropriate range restrictions, the hyperbolic functions all have inverses.
- Implicit differentiation yields differentiation formulas for the inverse hyperbolic functions, which in turn give rise to integration formulas.
- The most common physical applications of hyperbolic functions are calculations involving catenaries.
For the following exercises, find the derivatives of the given functions and graph along with the function to ensure your answer is correct.
For the following exercises, find the antiderivatives for the given functions.
For the following exercises, find the derivatives for the functions.
For the following exercises, find the antiderivatives for the functions.
For the following exercises, use the fact that a falling body with friction equal to velocity squared obeys the equation
For the following exercises, use this scenario: A cable hanging under its own weight has a slope
that satisfies
The constant
is the ratio of cable density to tension.
Questions & Answers
Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
can you send the book attached ?
Ariel
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2
find mu of x for y
U(x,y) = (xÃy)1/2
find mu of x for y
Desalegn
this is the study of how the society manages it's scarce resources
Belonwu
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
difference between firm and industry
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from
Qd 120 3P
to
Qd 90 3P
and the supply function has shifted from
QS
20 2P
to
QS
10 2P .
a) Find the effect of this change on price and quantity.
b) Which of the changes in demand and supply is higher?
explain standard reason why economic is a science
factors influencing supply
scares
means__________________ends
resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Why qualify 28 supplies
Milan
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
identify a demand and a supply curve
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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Source:
OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
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