Results 1 to 7 of 7

Math Help - Limits

  1. #1
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823

    Limits

    In the following library of functions, what are the values of c for which \lim_{x\to{c}}f(x)=f(c)?

    Polynomial function:

    f(x)=a_nx^n+...+a_1x+a_0

    Rational function:

    f(x)=\frac{p(x)}{q(x)}

    Trigonomic functions:

    f(x)=\sin{x}, f(x)\cos{x},
    f(x)=\tan{x}, f(x)=\cot{x},
    f(x)=\sec{x} , f(x)=\csc{x},

    Exponential functions:

    f(x)=a^x f(x)=e^x

    Natural logarithmic functions:

    f(x)=lnx

    I just kind of threw this out there guys because I'd like to improve my understanding of limits and continuity. Anyone who wants to tackle these has a thanks coming. More than one person's views are always welcome, so if anyone sees that the questions already been answered, don't let that stop you putting your spin on it. Thanks guys.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by VonNemo19 View Post
    In the following library of functions, what are the values of c for which \lim_{x\to{c}}f(x)=f(c)?

    Polynomial function:

    f(x)=a_nx^n+...+a_1x+a_0

    Rational function:

    f(x)=\frac{p(x)}{q(x)}

    Trigonomic functions:

    f(x)=\sin{x}, f(x)\cos{x},
    f(x)=\tan{x}, f(x)=\cot{x},
    f(x)=\sec{x} , f(x)=\csc{x},

    Exponential functions:

    f(x)=a^x f(x)=e^x

    Natural logarithmic functions:

    f(x)=lnx

    I just kind of threw this out there guys because I'd like to improve my understanding of limits and continuity. Anyone who wants to tackle these has a thanks coming. More than one person's views are always welcome, so if anyone sees that the questions already been answered, don't let that stop you putting your spin on it. Thanks guys.
    It will be true whenever f(x) is continous at c becuse that is the defintion of continuity at a point! i.e

    A function f(x) is continous at c if
    f(c)=\lim_{x \to c}f(x)


    so for the first one it is always true because polynomials are continous on the whole real line.

    2. It will be true anytime g(c) \ne =0

    ....

    I won't do the rest but what I said first will carry over to all of the other examples.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    What's the definiton of continuity over (a,b) then?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by VonNemo19 View Post
    What's the definiton of continuity over (a,b) then?
    If it is continous at each x \in (a,b)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    So, if I hear you correctly, if \lim_{x\to{c}}f(x)=f(c) for any and every value of c in (a,b), then f(x) is said to be continuous over (a,b). Can this be tested or only implied?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by VonNemo19 View Post
    So, if I hear you correctly, if \lim_{x\to{c}}f(x)=f(c) for any and every value of c in (a,b), then f(x) is said to be continuous over (a,b). Can this be tested or only implied?
    yes that is correct. Since any non empty inveteral that is not degenerate i.e [a,a] (only has one point) is uncountable there is no way to "test every point"

    So we have a bunch of functions we "know" are continous i.e like polynomials(and others on you list), and the fact that the product, sum, difference and quotient (as long as the denominator is not 0) of continous function is continous.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Thanks Man.

    What made you decide on the new photo?It's cool.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Using limits to find other limits
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 18th 2009, 05:34 PM
  2. Function limits and sequence limits
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: April 26th 2009, 01:45 PM
  3. HELP on LIMITS
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 23rd 2008, 11:17 PM
  4. Limits
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 21st 2008, 10:52 PM
  5. [SOLVED] [SOLVED] Limits. LIMITS!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 25th 2008, 10:41 PM

Search Tags


/mathhelpforum @mathhelpforum