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∫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
The functions {sinmx; cosmx}; m = 0,....∞ form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these
A 3 km pipe starts from point A end at point B Population = 3000 people Q = 300 L/day/person Roughness = cast ion pipe Length of the pipe = 3km Case 1 From A to B
Squeeze Theorem (Sandwich Theorem and the Pinching Theorem) Assume that for all x on [a, b] (except possibly at x = c ) we have, f ( x )≤ h (
Danielle requires knowing the distance around a basketball court. What geometry formula will she use? The perimeter of a rectangle is two times the length plus two times the wi
Consider R be a relation from A to B, that is, take R A Χ B. Then Domain R = {a: a € A, (a, b) € R for any b € B} i.e. domain of R is the set of all the first components of
Find out the greater of two consecutive positive odd integers whose product is 143. Let x = the lesser odd integer and let x + 2 = the greater odd integer. Because product is a
Pat is making a Christmas tree skirt. She needs to know how much fabric to buy. Using the example provided, calculate the area of the skirt to the nearest foot. a. 37.7 ft 2
L'Hospital's Rule Assume that we have one of the given cases, where a is any real number, infinity or negative infinity. In these cases we have, Therefore, L'H
Find the volume of a right circular cylinder: Calculate the volume and surface area of a right circular cylinder along with r = 3" and h = 4". Solution: V = πr 2
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