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Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
There are really three various methods for doing such integral. Method 1: This method uses a trig formula as, ∫sin(x) cos(x) dx = ½ ∫sin(2x) dx = -(1/4) cos(2x) + c
Unit circle A circle centered at the origin with radius 1 (i.e. this circle) is called as unit circle. The unit circle is very useful in Trigonometry. (b) x 2 + ( y - 3) 2
Suppose you are in the market for a new home and are interested in a new housing community under construction in a another city. a) The sales representative informs you that the
What is minimum spanning tree? Determine a railway network of minimal cost for the cities in the following graph using Kruskal's algorithm. Ans: Minimum spanning tree in a con
how do I round a # and decimal
A subset of the real line is called as an interval. Intervals are very significant in computing inequalities or in searching domains etc. If there are two numbers a, b € R such tha
/100*4500/12
The area of a rectangle gets decreased by 8 m2, if its length is decreased by 5 m and breadth increased by 3 m. If we enhance the length by 3 m and breadth by 2 m, the area is en
A 10 m ladder of 150N is placed at an angle 30degrees to a smooth wall at point A and the other end (point B) on the ground. Assume that the weight of the ladder acts at its mid po
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