Question

Evaluate:-

i) Sinx/2n​

Answer 1

Answer:Since (sin x)2 is almost always less than 1, when it is raised to the n→∞ power it will get closer and closer to 0.

The only places where this does not happen is when (sin x)2 = 1 in which case 1 raised to the n→∞ power is still 1.

So the function is equal to 0 everywhere except at specific x values where it is 1, these are the discontinuities.

Specifically, the discontinuities, f(x)=1, are when sin(x) = +/-1, that is when

x = 90 degrees + m*180 degrees

with m = ...,-3,-2,-1,0,-1,2,3,...

Or, as is more common in/beyond precalc,

x is in radians (π radians = 180 degrees) and the discontinuities are then at:

x = π/2 + m*π

Step-by-step explanation: