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Theorem If {a n } is bounded and monotonic then { a n } is convergent. Be cautious to not misuse this theorem. It does not state that if a sequence is not bounded and/or
Solve sin (α /7) =0 . Solution By Using a unit circle it isn't too difficult to see that the solutions to this equation are, α /7 = 0 + 2 ? n ⇒ α = 14 ? n
Arc Length for Parametric Equations L = ∫ β α √ ((dx/dt) 2 + (dy/dt) 2 ) dt Note: that we could have utilized the second formula for ds above is we had supposed inste
We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a
Based upon the primary sources, describe at least three characteristics that mark the early modern world as distinctly different than the Medieval world that preceded it. You might
Mount Everest is 29,028 ft high. Mount Kilimanjaro is 19,340 ft high. How much taller is Mount Everest? Subtract Mt. Kilimanjaro's height from Mt. Everest's height; 29,028 - 19
Example Show that p ( x ) = 2 x 3 - 5x 2 -10 x + 5 has a root somewhere in the interval [-1,2]. Solution What we're actually asking here is whether or not the function wi
show that one of the straight lines given by ax2+2hxy+by2=o bisect an angle between the co ordinate axes, if (a+b)2=4h2
Example of Imaginary Numbers: Example 1: Multiply √-2 and √-32 Solution: (√-2)( √-32) = (√2i)( √32i) =√64 (-1) =8 (-1) =-8 Example 2: Divid
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