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

Curve tracing, How we calculate region for curve tracing

How we calculate region for curve tracing

Application of interpolation and extrapolation, Application Interpolati...

Application Interpolation and extrapolation are widely used by businessmen, administrators, sociologists, economists and financial analysts. While interpolation hel

Find the maximum expected holdings, Problem: A person has 3 units of mo...

Problem: A person has 3 units of money available for investment in a business opportunity that matures in 1 year. The opportunity is risky in that the return is either double o

Linear programming problem., Ask question #Minimum 100 words acca paper mil...

Ask question #Minimum 100 words acca paper mill produces two grades of paper viz.,xand y.Bacause of raw material restrictions, it cannot produce more than 400 tones of grade x pape

Derivatives with chain rule, Chain Rule : We've seen many derivatives...

Chain Rule : We've seen many derivatives.  However, they have all been functions similar to the following kinds of functions. R ( z ) = √z      f (t ) = t 50

Harmonic mean-arthmetic geometric progression, Harmonic mean It is a m...

Harmonic mean It is a measure of central tendency which is utilized to determine the average increase rates for natural economies. This is defined like the reciprocal of the a

Npv, how to calculate the npv

how to calculate the npv

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