General Power Formula Examples

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Agency is a relationship based on an agreement authorizing one person, the agent, to act for another, the principal. For example an agent may negotiate and make contracts with third persons on behalf of the principal. Actions of an agent can obligate the principal to third persons. Actions of an agent may also give a principal rights against third persons.


An agency can be created for the purpose of doing almost any act the principal could do. However, there are some acts that must be done in person and cannot be done by an agent. Examples would be: testifying in court for another individual, making a will, and voting.


A general agent is authorized by the principal to transact all the affairs of a particular kind of business. For example, a person appointed as manager of a store is a general agent.


A special agent is authorized by the principal to handle a particular business transaction or perform a specific act. For example, a specific power of attorney appointing an agent (attorney-in-fact) to sell a particular piece of real estate or a certain car would be the appointment of a special agent.


A universal agent is authorized by the principal to do any act that can be delegated to a representative. An example would be giving a person a general power of attorney. This form is such a general power of attorney.

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The general power rule is a special case of the chain rule. It is useful when finding the derivative of a function that is raised to the nth power. The general power rule states that this derivative is n times the function raised to the (n-1)th power times the derivative of the function.

Integration: The General Power Formula. (We met this substitution formula in an earlier chapter: General Power Formula for Integration.) Our options are to either choose u = sin x, u = sin1/3 x or u = cos x.

The power rule for integrals allows us to find the indefinite (and later the definite) integrals of a variety of functions like polynomials, functions involving roots, and even some rational functions. If you can write it with an exponents, you probably can apply the power rule.

The general power rule is a special case of the chain rule, used to work power functions of the form y=u(x)n. The general power rule states that if y=u(x)n, then dy/dx=nu(x)n-1u'(x).

The general power rule of integration is another important formula of integration, and this rule needs th derivative of the given function within the problem. The general power rule of integration is of the form. 222bf(x)nf2032(x)dx=f(x)n+1n+1+c.

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The power rule is used to find the slope of polynomial functions and any other function that contains an exponent with a real number. 4.10.1 Find the general antiderivative of a given function. 4.10. A brief overview of the basic rules for exponents or powers. This new equation for power reveals that a powerful machine is both strong (big force) and fast (big velocity). A powerful car engine is strong and fast. This is the simplest formula for powers. 5. Example. Here R stands for resistance, V stands for potential difference and I stands for current. Since the derivative of a constant is 0, indefinite integrals are defined only up to an arbitrary constant.

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General Power Formula Examples