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Polar Coordinates Till this point we've dealt completely with the Cartesian (or Rectangular, or x-y) coordinate system. Though, as we will see, this is not all time the easie
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What is Angle Pairs in Parallel Lines ? Next, we introduce several angle pairs formed by transversals which are very important in our study of geometry. Alternate interior an
Evaluate the subsequent integral. ∫ (tan x/sec 4 x / sec 4 x) dx Solution This kind of integral approximately falls into the form given in 3c. It is a quotient of ta
Write an octave program that will take a set of points {x k , f k } representing a function and compute the derivative at the same points x k using 1. 2-point forward di erence
If cos?+sin? = √2 cos?, prove that cos? - sin? = √2 sin ?. Ans: Cos? + Sin? = √2 Cos? ⇒ ( Cos? + Sin?) 2 = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒
The region bounded by y=e -x and the x-axis among x = 0 and x = 1 is revolved around the x-axis. Determine the volume and surface area of this solid of revolution.
Draw the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation. Solution: y′ = y - x To draw direct
Question Solve the following functions for x (where x is a real number). Leave your answers in exact form, that is, do not use a calculator, show all working. (a) 3 x 3 x2 3
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