Recent content by gliteringstar

thank you :) But how do we find the graph of such a function?and if not the graph,can we get some idea about point of intersection of graph of this function with any of the axes?

...to be more precise... the cartesian equation of rectangular hyperbola in question is given by: xy=a^2 If we have it as (x-h)^4(y-k)=a^2,will the shape of graph of this rectangular hyperbola change?...the centre is different of course...it has shifted to (h,k) with the two parts of...

the general equation for rectangular hyperbola with vertical and horizontal asymptotes is given as : (x-h)(y-k)= some constant Is the following also an equation of rectangular hyperbola (x-h)^4(y-k)=some constant ? I am trying to find the shape of this curve,is it similar to that of...

for set : {(x,y): x^2+y^2=4} ,the complement is given by union of two open sets {{(x,y):x^2+y^2>4}union {(x,y):x^2+y^2<4}} which is an open set as per the definiton hence, {(x,y): x^2+y^2=4} is a closed set!

An open set is a set which is neighbourhood of all its points a) {(x,y):x^2+y^2>4} is an open set because it is neighbourhood of all its points A closed set is a set if its complement is an open set b){(x,y):x^2+y^2<=4}is a closed set because its complement {(x,y):x^2+y^2>4} is an...

Thanks a lot! The wonderful explanation given by you has cleared all my doubts regarding positive number epsilon :) So the bottomline is no matter whatever be our x whether it is in the middle of our set or near the end-points,there always will exist a positive number e,such that this new...

A set is open if it is a neighbourhood of each of its points.Is this similar to saying that a set is open if it contains all of its interior points?If yes,then can we proceed in the following way: the set {(x,y): x^2+y^2>4} is in R^2 If i take a point ,say (q,s) which lies very close...

"what if we take our positive number to be .2 in this case 2.1 belongs to (1.8,2.4)which isn't a subset of (2,3) is there a restriction that we need to choose a very small positive number?" there is a mistake, the open interval obtained should be (2.1-.2,2.1+.2)= (1.9,2.3) instead of...

neighbourhood of a point A set T (a subset of R) is called neighbourhood of a point s if for any positive number e>0,the open interval (p-e,p+e) is a subset of T It is also given that any open interval is neighbourhood of all its points. let us take an example (2,3) is an open...

a) {(x,y):x^2+y^2>=4} x^2+y^2= 4 is equation of a circle in 2-dimensional space, with radius 2 and centre at (0,0) the set given above shall include all points on the circle and beyond (extending to infinity);if i take a boundary point say, (2,0) from this set,then this should be...

How do we define closed sets? A closed set is one that includes all its boundary points,is this definition right? which of the following are closed sets? a){(x,y): x^2+y^2 >=4} b){(x,y):x^2+y^2<=4} c){(x,y):x^2+y^2=4}

whenever a function is expressed in terms of another function,how do we find whether the function is increasing or decreasing? say ,for example ,we have : h(x)= f(2x)+f(x) pls tell anyone,what procedure we need to follow to find whether the above given function is...

thanks chris for your reply,but won't it take time to solve it through this method? what i mean is-we know the graph of y=log x also,the equation of logarithmic function can be written as: some constant-log x= y,but by plotting it through putting various values of x,won't it be time...

I am facing difficulty in graphing this logarithmic function: some constant= y + log x what all steps are required to graph such a function?