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

How to raise powers of monomials, How to raise Powers of Monomials ? To ...

How to raise Powers of Monomials ? To raise a monomial to a certain power: Step 1: Place the entire monomial inside parentheses, and place the desired power outside the paren

DECIMALS, the mass of a container is 5.81kg when full with sugar .the mass ...

the mass of a container is 5.81kg when full with sugar .the mass of container is 3.8kg when 3/8 of the sugar is removed.what is the mass of empty container

Two even digits , Find the number of six-digit positive integers that can b...

Find the number of six-digit positive integers that can be formed using the digits 1,2, 3, 4, and 5 (every of which may be repeated) if the number must start with two even digits o

Show that positive integers is divisible by 6, Show that the product of 3 c...

Show that the product of 3 consecutive positive integers is divisible by 6. Ans: n,n+1,n+2 be three consecutive positive integers We know that n is of the form 3q, 3q +1

Sum of a number of terms in g.p., We know that the terms in G.P. are:...

We know that the terms in G.P. are: a, ar, ar 2 , ar 3 , ar 4 , ................, ar n-1 Let s be the sum of these terms, then s = a + ar + ar 2

Linear probability model, Pepsi:               A dummy variable where 1 den...

Pepsi:               A dummy variable where 1 denotes choice of Pepsi by the i-th customer and 0 otherwise Price_P:           The price of a 2-liter bottle of Pepsi at the time

Divide by 1-digit numbers, which experession can be used to check the quoti...

which experession can be used to check the quotient 646 divided by 3

Example on abels theorem, Without solving, find out the Wronskian of two so...

Without solving, find out the Wronskian of two solutions to the subsequent differential equation. t 4 y'' - 2t 3 y' - t 8 y = 0 Solution : First thing that we want to d

#algebra, what is the answer of 6_5x9_4x3(1_2)

what is the answer of 6_5x9_4x3(1_2)

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