Reeya

My book says it's zero at x= -ln(2) but I keep getting x= ln(1/2). Help?

What is the probability that the word consists of all different words?

The Smyth report states that battleships despite being immune to nuclear attack(given their ability to disperse quickly aka tactful dispersion) are redundant when it comes to countering nuclear attacks. Whereas air-superiority might provide a certain level of security to a nation. Why is naval power so useless in nuclear stand-offs?

You have five iron pipes of diameter 1cm, 3cm, 5cm, 8cm and 10cm. Each pipe's length is 1m. Develop a useful product using above pipes.

I have thought a possible product but I would like to know what others have to say.

integrate :

sqrt(x^2-x+1)/(x-1)

f:R->R defined by f(x)= x/(x^2+1)

Check whether it is an onto function?

So, to be an onto function its range should be equal to its co-domain i.e f(x)=y

=> x/(x^2+1)=y

=> x^2y+y=x

=> x^2y-x= -y

=> x(xy-1)= -y

=> x= -y/(xy-1)

If f is an onto function then for every y belonging to R(co-domain) there should be x belonging to R(domain) such that f(x)=y i.e range= co-domain??

I don't know how to proceed any further and I am not very sure that whatever i have done is correct in the slightest manner....please help asap?

Let S be a set of all rational numbers except 1 and * be defined on S by a*b=a+b-ab, for all a,b∈ S.

Prove that: * is a binary operation on S.

can you explain the relation between the two? plz keep the explanation simple.thanks.

If y=m(1+ √(x^2-1))

prove that (x^2-1)d2y/dx2+xdy/dx=m^2

Q1.if A and B are square matrices of order 3 such that |A|=-1 and |B|=4, then what is the value of |3AB|?

Q2.If A=[a 0] is a 2x2 matrix, find A^16?

[0 0]

I took maths as one of my main subjects in grade 11. Now that I am in grade 12 I have realized that it was a big mistake.I have always been a bright student and have always secured the highest marks in all my classes. But I have always had a phobia of maths. In grade 11, I told myself that I can be good at it if I try harder. I worked very hard. Worked day and night. But on the day of my final exam I was overcome with anxiety and missed my exam. I have never been good at maths no matter how hard I try. Should I just give up?

f(x)= sinx(1+cosx) and x belongs to (0,pi/2)

My answer:

f'(x)= cosx(1+cosx)+ sinx(-sinx)

= cosx+cos^2x-sin^2x

=cosx+cos2x

For f(x) to be increasing: f'(x)>0

=> cosx+cos2x>0

What should I do next??

I) f(x)= x|x|

II) f(x)= sinx+|sinx|

let C be a parametrically defined curve as x=acos^3x, y= asin^3x, X BELONGS TO [0,PI/2] .Determine a point P on C, where the tangent to C is parallel to the chords joining the points (a,0) and (0,a)

Find the derivative of 1/3pi.h^4.tan^3x where x doesn't change??

Discuss the continuity and differentiability of the function f(x)=|x|+|x-1| in the interval (-1,2).

I have solved questions where piece-wise functions are given but I don't know how to solve for differentiability when intervals are given?

Plz help?

Q: If y=(1+x)(1+x^2)(1+x^4).....(1+x^2^n) find dx/dy.

In my book, (1-x) has been multiplied and divided to the expression:

y=[(1-x)(1+x)(1+x^2)(1+x^4).....(1+x^2^n) ]/(1-x)

Then, the next step says that:

y= [1-x^2^(n+1)]/(1-x)

How did they find the nth term? Please explain? Is there not a way to find the nth term ( which in turn I can use to dind the derivative) without multiplying and dividing

(1-x)??

I have to check whether the following function is differentiable at x=2 or not:

f(x)= x-1 if x<2

and 2x-3 it x>=2

I have correctly calculated the Right Hand Derivative which came out to be 2.

My Left Hand Derivative is coming out to be -1, which is wrong.(my book says its 1. I am pretty sure it is not misprinted)

Here's how I calculated the LHD:

lim(h->0) [f(2-h)-f(2)]/h

lim(h->0) [ ({2-h}-1)-{2(2)-3) ]/h

lim(h->0) [2-h-1-4+3]/h

lim(h->0)[-h+1+3-4]/h

lim(h->0) [-h]/h

= -1

Please tell me where i am wrong??

Given f(x)= 1/(x+2)

Find the points of discontinuity of f(x) and f(f(x)).

Please explain how to do this question?