I have one problem,
ajax url not going to my ajax.php.

please any body help me

<html>
<head>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<script>
$(document).ready(function(){
    $('.button').click(function(){
        var clickBtnValue = $(this).val();
        var ajaxurl = 'ajax.php',
        data =  {'action': clickBtnValue};
        $.post(ajaxurl, data, function (response) {
            // Response div goes here.
            alert("action performed successfully");
        });
    });

});
</script>
</head>

<body>
<input type="submit" class="button" name="insert" value="insert" />
<input type="submit" class="button" name="select" value="select" />
</body>
</html>

My ajax page is

<?php
if (isset($_POST['action'])) {
    switch ($_POST['action']) {
        case 'insert':
            insert();
            break;
        case 'select':
            select();
            break;
    }
}

function select() {
    echo "The select function is called.";
    exit;
}

function insert() {
    echo "The insert function is called.";
    exit;
}
?>

Actually your codes work fine. What you should do is to handle your reponse well. I ammend a little of your codes for testing.

<html>
<head>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<script>
$(document).ready(function(){
    $('.button').click(function(){
        var clickBtnValue = $(this).val();
        var ajaxurl = 'ajax.php',
        data =  {'action': clickBtnValue};
        $.post(ajaxurl, data, function (response) {
            // Response div goes here.
            document.getElementById("myDiv").innerHTML=response;
            alert("action performed successfully");
        });
    });
});
</script>
</head>
<body>
<div id = 'myDiv'></div>
<input type="submit" class="button" name="insert" value="insert" />
<input type="submit" class="button" name="select" value="select" />
</body>
</html>

If it still not working, maybe your ajax.php is not same directory to your html? If that is in the case, you should change the 'ajax.php' to relative paths

Very thanks for giving response.
It is working.

If the issue is solved, please do mark this article as 'solve', thanks