Functions of limits, Mathematics

Assignment Help:

Following is some more common functions that are "nice enough".

  • Polynomials are nice enough for all x's.
  • If f ( x) = p ( x ) /q (x ) then f(x) will be nice enough provided p(x) and q(x) both are nice enough & if we don't get division by zero at the point we're evaluating at.
  • cos ( x ) , sin ( x ) are nice enough for all x's
  • sec ( x ) , tan ( x ) are nice enough provided x ≠ ........., - 5 ?/2 , - 3 ?/2 , ?/2 , 3 ?/2 , 5 ?/2 , ...... In other terms secant & tangent are nice enough everywhere cosine isn't zero. To illustrates why recall that these are both actually rational functions & that cosine is in the denominator of both then go back up & look at the second bullet above.
  • csc ( x ) , cot ( x ) are nice enough provided x ≠ ......, -2 ? , - ? , 0, ? , 2 ? ,..... In other terms cosecant & cotangent are nice enough everywhere sine isn't zero
  • is nice enough for all x if n is odd.
  • if n is even then is nice enough for x ≥ 0. Here we need x ≥ 0 to ignore having to deal along with complex values.
  • a x , ex are nice enough for all x's
  • logb x, ln x are nice enough for x>0. Recall we can just plug positive numbers into logarithms & not zero or negative numbers.
  • Any sum, difference or product of the functions will also be nice enough.
  • Quotients will be nice enough provided we don't obatin division by zero upon evaluating the limit.

The last bullet is significant. It means that for any combination of these functions all we have to do is evaluate the function at the point in question, ensuring that none of the restrictions are violated. It means that now we can do a large number of limits.


Related Discussions:- Functions of limits

Example of circle graphs, Q. Example of circle graphs? Ans. The Un...

Q. Example of circle graphs? Ans. The United States Government pays obligations annually, called "outlays". Medicare contributes to the health and well being of aged an

What is a system of equations?, What is a System of Equations? And its Solu...

What is a System of Equations? And its Solution? Here is an example of a system of equations (also called a simultaneous system of equations) x 2 + y = 3

Ratio, how to do them?

how to do them?

Metric Units, How do I convert metric units?

How do I convert metric units?

Illustrate exponential distribution, Q. Illustrate Exponential Distribution...

Q. Illustrate Exponential Distribution? Ans. These are two examples of events that have an exponential distribution: The length of time you wait at a bus stop for the n

Differential equation of newton’s law of cooling , 1. A direction ?eld for...

1. A direction ?eld for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step

Angles, how do you workout the value of the missing angle

how do you workout the value of the missing angle

Long distance calls cost x cent how much 5-minute call cost, A long distanc...

A long distance calls costs x cents for the first minute and y cents for every additional minute. How much would a 5-minute call cost? The cost of the call is x cents plus y ti

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd