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

Which of the subsequent binomials could represent the length, The area of a...

The area of a rectangle is represented through the trinomial: x 2 + x - 12. Which of the subsequent binomials could represent the length and width? Because the formula for the

Problem word solving, Mrs. Jones and Mr. Graham had the same amount of mone...

Mrs. Jones and Mr. Graham had the same amount of money at first. After Mrs. Jones bought a computer that cost $2,055, she had 1/4 as much money as Mr. Graham. How much money di

Prime Ideals, Given a standard 2x3 matrix show the ideal formed by the 2x2 ...

Given a standard 2x3 matrix show the ideal formed by the 2x2 minors is Prime.

Limit problem, limit x-a/|x-a| equals x-a [a]a [b]0 [c]-a [d]none 0f these

limit x-a/|x-a| equals x-a [a]a [b]0 [c]-a [d]none 0f these

Linear algebra, solve for k such that the system 4x+ky=6 kx+y=-3

solve for k such that the system 4x+ky=6 kx+y=-3

Times, teach me how to o times 7s

teach me how to o times 7s

Right angle trigonometry, use the Pythagorean Theorem to find the length of...

use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of the given angle. give an exact answer with a rational denomina

Decision theory, Decision Theory Decisions There are many types of ...

Decision Theory Decisions There are many types of decision making 1.      Decision making under uncertainty It refer to situations where more than one outcome can r

Famous Numbers, Do you provide the answers to the Famous Numbers Exercise?

Do you provide the answers to the Famous Numbers Exercise?

Law of Iterative Expectation, #quesSuppose we have a stick of length L. We ...

#quesSuppose we have a stick of length L. We break it once at some point X ~ Unif(0;L). Then we break it again at some point Y ~ Unif(0;X). Use the law of iterated expectation to c

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