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

Applications of markov chains in business, please help me in my assignment,...

please help me in my assignment, explain Applications of Markov Chains in Business.

Find out the area under the parametric curve, Find out the area under the p...

Find out the area under the parametric curve given by the following parametric equations.  x = 6 (θ - sin θ) y = 6 (1 - cos θ) 0 ≤ θ ≤ 2Π Solution Firstly, notice th

Parabola, write the equation of parabola of vertex(2,-3)and focus(_1,1)

write the equation of parabola of vertex(2,-3)and focus(_1,1)

Comparison test - sequences and series, Comparison Test Assume that we...

Comparison Test Assume that we have two types of series ∑a n and ∑b n with a n , b n ≥ 0 for all n and a n ≤ b n for all n.  Then, A.  If ∑b n is convergent then t

Non-homogeneous differential equations, The Definition- The definition of ...

The Definition- The definition of the Laplace transforms. We will also calculate a couple Laplace transforms by using the definition. Laplace Transforms- As the earlier secti

Function, definition and examples and types

definition and examples and types

Statistics, How many 4 digit numbers can be formed using the numbers: 1 – 7...

How many 4 digit numbers can be formed using the numbers: 1 – 7. Repeated numbers CAN NOT be used

Pair of straight line, a pair of straight lines are drawn through the origi...

a pair of straight lines are drawn through the origin forms with the line 2x+3y=6 an isoceles triangle right angled at origin find the equation of pair of straight line?

Naming fractions greater than 1, the 10 miles assigned to the chess club st...

the 10 miles assigned to the chess club start at the 10 mile point and go to the 20 mile point when the chess club members have cleaned 5/8 of their 10 mile section between which m

How long will it take him to plow 21 acres, Mr. Brown plowed 6 acres in 1 h...

Mr. Brown plowed 6 acres in 1 hour. At this rate, how long will it take him to plow 21 acres? Mr. Brown plows 6 acres an hour, so divide the number of acres (21) through 6 to f

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