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

Jason 10 two-point or 2 three-point how many points score, Jason made 10 tw...

Jason made 10 two-point baskets and 2 three-point baskets within Friday's basketball game. He did not score any other points. How many points did he score? Find out the number

Solution Of Rectilinear Figures, Find the number of square feet of pavement...

Find the number of square feet of pavement required for the shaded portion of the streets shown in the figure, all the streets being 50 feet wide.

Fractions, how do you do fractions mixed numbers and how do you add and sub...

how do you do fractions mixed numbers and how do you add and subtract fractions.

Robin''s nest nursing home had a fundraising target, The Robin's Nest Nursi...

The Robin's Nest Nursing Home had a fundraising target of $9,500. By the end of the fundraiser, they had exceeded their goal through $2,100. How much did they raise? Exceeded

Analyze the dynamic path of pork prices, A well-known simple model, applica...

A well-known simple model, applicable for analysing boom-bust cycles in agriculture, but extendable to analysing boom-bust cycles in many different areas of economics is the hog cy

Method to solve binomials of second degree, In this part we look at a...

In this part we look at another method to obtain the factors of an expression. In the above you have seen that x 2 - 4x + 4 = (x - 2) 2 or (x - 2)(x - 2). If yo

Exponents, i need help with exponents and how to add them

i need help with exponents and how to add them

Find the length of the second diagonal, Find the length of the second diago...

Find the length of the second diagonal of a rhombus, whose side is 5cm and one of the diagonals is 6cm.

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