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Determine the unit tangent at the point where t=2 on the curve
x=t2+1
x=t2+1
,
y=4t−3
y=4t−3
and
z=2t2−6t
z=2t2−6t

.If
A=5t2+tj−t3k
A=5t2+tj−t3k
and
B=sinti−costj
B=sin⁡ti−cos⁡tj

. evaluate
ddt(A⋅B)

If
A=5t2+tj−t3k
A=5t2+tj−t3k
and
B=sinti−costj
B=sin⁡ti−cos⁡tj

. evaluate
ddt(A×B)

If
A=5t2+tj−t3k
A=5t2+tj−t3k
and
B=sinti−costj
B=sin⁡ti−cos⁡tj
. evaluate
ddt(A⋅A)

If
A=sinui+cosuj+uk
A=sin⁡ui+cos⁡uj+uk
,
B=cosui−sinuj−3k
B=cosui−sinuj−3k
and
C=2i+3j−k
C=2i+3j−k

, evaluate
ddu(A×(B×C))
ddu(A×(B×C))
at u=0

Write an “active password checker” in PHP. The purpose of an active password checker is to prevent the user from selecting a password or password phrase that is easily guessed. This may be done by comparing potential passwords with a dictionary, examining the mix of characters selected, checking user information, and so on.

JS: /*Dynamically add two buttons on page load and these buttons should call getImage1Data and getImage2Data in the JS file. Please don't use any libraries.*/
6) Write Sample code for dynamically creating image tag for first image to the div.
7) Add background to right div with src from 2nd request to cover parent background.

JavaScript File :

function getImage1Data(){
var image1Src;
var xhttp = new XMLHttpRequest();
xhttp.open("Get", 'some Url', false);
xhttp.send(null);
image1Src = xmlhttp.responseText; //Assume src = 'myFirstImg.png', 200x200 px
}


function getImage2Data(){

var xhttp = new XMLHttpRequest();
xhttp.onreadystatechange = function(){
if(xmlhttp.readyState == 4 && xmlhttp.status == 200)
getSrc(xmlhttp.responseText);
}
xhttp.open("Get", 'some Url', true);
xhttp.send(null);
}

function getSrc(text){
image2Src = text; //Assume src = 'myLastImg.png', 10x10 px
}

How to load script file in jQuery ?
I need to load the script only when button is clicked .
<script type="text/javascript" src="<%=request.getContextPath()%>/resources/jquery/jquery-1.9.1.js"></script>
<script type="text/javascript" src="${pageContext.servletContext.contextPath}/resources/js/jquery.slimscroll.min.js"></script>

I am unable to load the script file wen the button is clicked on actual page