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

Calculate the area and perimeter of a square, Calculate the area and perime...

Calculate the area and perimeter of a square: Calculate the area and perimeter of a square with w = 5´ and l = 6´.  Be sure to involved units in your answer. Solution:

Share and divivdend, i m making a project on share and dividend. will u pls...

i m making a project on share and dividend. will u pls give the all of 10pages information ?

Cirlce Division, How can i calculate arc length for dividing a circle into ...

How can i calculate arc length for dividing a circle into 10 parts

Average function value of even and odd function, Average Function Value ...

Average Function Value The first application of integrals which we'll see is the average value of a function. The given fact tells us how to calculate this. Average Functi

Write following in terms of simpler logarithms, Write following in terms of...

Write following in terms of simpler logarithms.  (a) log 3 (9 x 4    / √y) Solution log 3 (9 x 4 / √y) =log ­ 3 9x 4 -  log  y (1/2) =log ­ 3 9 + log ­ 3 x 4

4.4238/[1.047+{1.111*[9.261/7.777]}*1.01, Ask question #Min 4.4238/[1.047+{...

Ask question #Min 4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

D, #quwhat is4 5/7 of 2/3estion..

#quwhat is4 5/7 of 2/3estion..

Differential equation.., 3.6Find the general solution of the differential e...

3.6Find the general solution of the differential equation Y" + 4y = Sec2 2x

Determine the size of belt, On a piece of machinery, the centers of two pul...

On a piece of machinery, the centers of two pulleys are 3 feet apart, and the radius of each pulley is 6 inches. Determine the size of belt (in feet) is required to wrap around bot

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