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Equivalent or Equal sets Two sets C and D are said to be equal whether every member of set C belongs to D and every member of set D belongs also to C.
∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cosec2x - cot2x] + c = 1/2 log[tan x] + c Detailed derivation of ∫cosec x dx = ∫cosec x(cosec x - cot x)/(cosec x - cot x) dx = ∫(cosec 2 x
-6x-4y=-6 x+2y=-3
16 times 4
A sphere and a cube have equal surface areas. Show that the ratio of the volume of the sphere to that of the cube is √6 : √π. Ans: S.A. of sphere = S.A of cube 4π r 2
Graph for the Sequence First we wish to think about the term graphing a sequence. To graph the sequence {a n } we plot the points {n, a n } as n ranges over every possible valu
1. Sketch the Spiral of Archimedes: r= aθ (a>0) ? 2: Sketch the hyperbolic Spiral: rθ = a (a>0) ? 3: Sketch the equiangular spiral: r=ae θ (a>0) ?
Graph y = tan ( x ). Solution In the case of tangent we need to be careful while plugging x's in since tangent doesn't present wherever cosine is zero (remember that tan x
If 4x^4+9x^4=64 then the maximum value of x^2+y^2 is solution) From the eq. finding the value of x^2 and putting it in x^2 + y^2.we get 2nd eq. differentiating that and putting
Financial institutions often create synthetic instruments out of existing instruments. In this case an investment bank plans to buy Treasury Bonds with 20-year maturities at their
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