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

Define a hamilton path, Define a Hamilton path. Determine if the following ...

Define a Hamilton path. Determine if the following graph has a Hamilton circuit. Ans: A path is known as a Hamiltonian path if it consists of every vertex of the graph e

Coordinate geometry, find the value of x for which the distance between the...

find the value of x for which the distance between the points p(4,-5) and q(12,x) is 10 units

Limits at infinity, Limits At Infinity, Part I : In the earlier section w...

Limits At Infinity, Part I : In the earlier section we saw limits which were infinity and now it's time to take a look at limits at infinity.  Through limits at infinity we mean

Comparison test or limit comparison test, Comparison Test or Limit Comparis...

Comparison Test or Limit Comparison Test In the preceding section we saw how to relate a series to an improper integral to find out the convergence of a series.  When the inte

What is the probability in which she gets heads further flip, Jennifer ?ipp...

Jennifer ?ipped a coin three times and got heads each time. What is the probability in which she gets heads on the further ?ip? The probability of heads does not modify based o

Binary to decimal, 01010011 01100101 01101101 01110000 01100101 01110010 00...

01010011 01100101 01101101 01110000 01100101 01110010 00100000 01000110 01101001 00100001

Finish the work., six men and Eight boys can finish a piece of work in 14 d...

six men and Eight boys can finish a piece of work in 14 days while  eight men and twelve boys can do it in 10 days. Find the time taken by  1man alone and that by 1boy alone to fin

Calculus three, i would like answers to these questions i will give you as ...

i would like answers to these questions i will give you as soon as possible

Determine the marginal probability distributions, (1)   The following table...

(1)   The following table gives the joint probability distribution p (X, Y) of random variables X and Y. Determine the following: (a) Do the entries of the table satisfy

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