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Q. Define Period, Amplitude and Phase Shift?
Ans.
Period, amplitude and phase shift are used when describing a sinusoidal curve
The period of a function is the smallest number p for which f( x + p) = f(x) for each x for which is defined.
The function sin(x) repeats every degrees, sin (x +) = sin(x). It is also clear by the graph that 2p is the smallest number for which this is true. The period of sin(x) is 2Π.
The amplitude of a sinusoidal wave is the distance from the central axis (the x-axis in this case) and the maximum or minimum value of the wave.
The phase shift of a curve is the shift, left or right, of the base curve.
Ratio - situations in which we need to compare two quantities in terms of their ratio. (e.g., if Munna weighs 40 Kg. and Munni weighs 50 Kg., find the ratio of their weights.)
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The diagram below shows the cross section of a pipe 1/2 inch thick that has an inside diameter of 3 inches. Determine the area of the shaded region in terms of π. a. 8.75π i
112 in 8
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introduction
f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
Determine the general solution to 2t 2 y'' + ty' - 3y = 0 It given that y (t) = t -1 is a solution. Solution Reduction of order needs that a solution already be iden
Interpretations of derivatives. Example: Find out the equation of the tangent line to x 2 + y 2 =9 at the point (2, √5 ) .
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