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

Prove that one of three consecutive integers divisible by 3, Prove that one...

Prove that one of every three consecutive integers is divisible by 3. Ans: n,n+1,n+2 be three consecutive positive integers We know that n is of the form 3q, 3q +1, 3q +

How many inches is the smaller dimension of the decreased, A photographer d...

A photographer decides to decrease a picture she took in sequence to fit it within a certain frame. She requires the picture to be one-third of the area of the original. If the ori

Unconditional and conditional probability, Two events A and B are ind...

Two events A and B are independent events if the occurrence of event A is in no way related to the occurrence or non-occurrence of event B. Likewise for independent

Word problems, A patient will receive hemodialysis for 2.5 hours. The amoun...

A patient will receive hemodialysis for 2.5 hours. The amount of fluid removed per hour is 1.4 liters. The total amount removed in liters, will be

Math help, Can you help me with what goes into 54

Can you help me with what goes into 54

Maths For Fun, Ask Suppose I offer you a loan to start a safety matchstick ...

Ask Suppose I offer you a loan to start a safety matchstick production unit on the following terms: I shall first advance you Rs.50,000/- to set up your unit, and wait for 3 month

Area with polar coordinates - parametric equations, Area with Polar Coordin...

Area with Polar Coordinates In this part we are going to look at areas enclosed via polar curves.  Note also that we said "enclosed by" in place of "under" as we usually have

Trigonmetry, On your geometry test you have two triangles: ?ABC and ?MNO. Y...

On your geometry test you have two triangles: ?ABC and ?MNO. You are told that ?A ? ? M and that ?B ? ? N. Which statement is also true?

Calculate log equation, Calculate log equation: Calculate log 10 2 - ...

Calculate log equation: Calculate log 10 2 - log 10 3. Solution: Rule 2. log 10   (A/B): log 10   A - log 10   B log 10   2 - log 10   3 = log 10   (2/3) =

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