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proof of various integral factsformulaspropertiesin this section weve found the proof of several of the properties we saw in the integrals section
rolles theorem assume fx is a function which satisfies all of the following1 fx is continuous in the closed interval ab2 fx is differentiable in
fermats theorem if fx has a relative extrema at x c and fprimec exists then x c is a critical point of fx actually this will be a critical point
proof of limqrarr0 cosq -1q 0we will begin by doing the followinglimqrarr0 cosq -1q limqrarr0cosq - 1cosq 1q cosq 1 limqrarr0cos2q - 1 q cosq
in x-ray tube when high speed electrons strike the target they move into the target they lose their kinetic energy and come to rest inside the solid
i x-rays are electromagnetic waves with wavelength lie among 01aring - 100aringii x-rays is invisibleiii they always go in a straight line
depending upon the penetration power there are two parts of x-rayshard x-raysmore penetration powermore frequency of the order of asymp 1019 hzlesser
chain rule if fx and gx are both differentiable functions and we describe fx f gx so the derivative of fx is fprimex f primegx
quotient rule fg fg - fgg2here we can do this by using the definition of the derivative or along with logarithmic definitionproof here we do the
x-rays was discovered by scientist rontgen thats why they are also known as rontgen pulsesrontgen discovered that when pressure inside a discharge
product rule f gprime f prime g f gprimeas with above the power rule so the product rule can be proved either through using the definition of the
power rule dxndx nxn-1there are really three proofs which we can provide here and we are going to suffer all three here therefore you can notice all
proof of the derivative of a constant dcdx 0it is very easy to prove by using the definition of the derivative therefore define fx c and the
proof of constant times a function cfxprime cf primexit is very easy property to prove using the definition given you a recall we can factor a
proof of sumdifference of two functions fx gxprime f primex g primex it is easy adequate to prove by using the definition of the
grimm plc grimm has the following transactionsa on 1st january 2010 grimm issued 400000 convertible pound1 6 debentures for pound600000 the
theorem from definition of derivative if fx is differentiable at x a then fx is continuous at x aproof since fx is differentiable at x a we
proof of various derivative factsformulaspropertiesunder this section we are going to prove several of the different derivative facts formulas orand
go back to the complex numbers code in figures 50 and 51 of your notes add code fragments to handle the following1 a function for adding two complex
proof of various limit propertiesin this section we are going to prove several of the fundamental facts and properties about limits which we saw
a device which changes light energy into electrical energy is known as photoelectric cell it is also known as photocell or electric
it is the phenomenon of emission of electrons from the surface of metals when light radiations electromagnetic radiations of suitable frequency drop
according to eisensteins quantum theory light propagates in the bundles of power every packet being called as photon and possessing
it is explained by heisenbergs uncertainty principle it is impossible to calculate simultaneously both the position and the momentum of the
i a matter pulse is not electromagnetic in behaviorii practical observation of matter waves is possible only when the de-broglie wavelength is of the