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

Pair of straight line, show that one of the straight lines given by ax2+2hx...

show that one of the straight lines given by ax2+2hxy+by2=o bisect an angle between the co ordinate axes, if (a+b)2=4h2

Geometry, P and Q are the points (12,0) and (0,-5) respectively,find the le...

P and Q are the points (12,0) and (0,-5) respectively,find the length of the median through the origin O of the triangle OPQ

Derivatives, What are the ingredients of a Mathematical Model? What is a mo...

What are the ingredients of a Mathematical Model? What is a model?

Study market, what toold we need to study market

what toold we need to study market

Estimate how much did the budget increase, Previous year's budget was 12.5 ...

Previous year's budget was 12.5 million dollars. This year's budget is 14.1 million dollars. How much did the budget increase? Last year's budget must be subtracted from this y

Line with rise of five and run of two is positive, Draw a graph which has s...

Draw a graph which has slope of a line with rise of five and run of two is positive.

1 application of complex analysis in THERMODYNAMICS, Hi, this is EBADULLA ...

Hi, this is EBADULLA its about math assignment. 1 application of complex analysis used in thermodynamics. . what all uses are there in that... plz let mee know this answer.

Find the sum of given equation upto n limit, Find the sum of (1 - 1/n ) + (...

Find the sum of (1 - 1/n ) + (1 - 2/n ) + (1 - 3/n ) ....... upto n terms. Ans: (1 - 1/n ) + (1 - 2/n ) - upto n terms   ⇒[1+1+.......+n terms] - [ 1/n + 2/n +....+

Assumptions and application of t distribution, Assumptions and Application ...

Assumptions and Application of T Distribution Assumptions of t distribution 1. The sample observations are random 2. Samples are drawn from general distribution 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