Recent content by seshikanth

gentle reminder

Can anyone have a look at this? Thanks,

Hi Can anyone please clarify the following? Let there by a rolling cylinder on an inclined plane. Let the solid cylinder(with Center O) on the inclined plane has Center of gravity at a distance 'c' slightly above O. If the cylinder is displaced slightly through an angle θ then [Let N =...

Got it! Thanks!

Gentle reminder

Can u please throw some light on this? Thanks

As we know grad F (F surface) is in normal direction. But we also have (grad F(r)) x r = F'(r) (r) x r = 0 this implies grad F is in direction of r i.e., radial direction. Radial and normal directions need not be same. Can any öne clarify THE DIRECTION OF GRAD VECTOR? Thanks,

As we know grad F (F surface) is in normal direction. But we also have (grad F(r)) x r = F'(r) (r) x r = 0 this implies grad F is in direction of r i.e., radial direction. Radial and normal directions need not be same. Can any öne clarify THE DIRECTION OF GRAD VECTOR?

One more question: Please correct me if i am wrong here- "If a function f is Riemann integrable on closed and bounded interval [a,b] then f is continuous on [a,b] and also the converse is also true" i.e., Riemann integrable <=> f being continuous

Got it!

If the norm shrinks and shrinks tending towards zero, How can the number of points in the partition be finite? This is where i am thinking! (Lower Darbaux sum will be equal to Upper Darbaux sum only when the number of intervals tends to infinite)

Can you please elaborate? The norm of partition tending to zero implies that the number of points in the partition also tends to infinite. Thanks,

Regarding "Riemann integration defination" Hi, I did not understand the following: We have : Partition is always a "finite set". A function f is said to Riemann integrable if f is bounded and Limit ||P|| -> 0 L(f,P) = Limit||P|| -> 0 U(f,P) where L(f,P) and U(f,P) are...

Hi, If we consider Rolle's Theorem: "If [1] f is continuous on [a, b], [2] differentiable in (a,b), and [3]f (a) = f (b), then there exists a point c in (a, b) where f'(c) = 0." In the above theorem, i did not get why condition [1] is needed as we have differentiability =>...

Homework Statement I am trying to solve a question from Abstract Algebra by Hernstein. Can anyone give me hint regarding the following: Show that a group can not be written as union of 2 (proper) subgroups although it is possible to express it as union of 3 subgroups? Thanks...