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As it appears, you seem to be seeking the limit of sin(4x)*sin(6x) as x tends to 0.
Both components of the product tend to 0 as x tens to 0 and so the limit is 0. Bit I suspect that is not the limit that you are looking for.
You would probably use a power-reduction trig identity to solve this equation. This states that sin2(x) = (1 - cos(2x))/2 Therefore, sin2(2x) = (1 - cos(4x))/2, or (1/2)(1 - cos(4x)) So, ∫ (1/2)(1 - cos(4x)) dx = (1/2) ∫ (1 - cos(4x)) dx. Then, ∫ (1-cos4x)dx = x - (1/4)sin(4x) + c Now, multiply that by (1/2) to get: (x - (sin(4x)/4) + c)/2 Since c is an arbitrary constant, we have: ½(x - sin(4x) / 4) + c OR 1/8 * (4x - sin(4x)) + c
I'm sorry the question is not correctly displayed. If f(x) = cos(2x).cos(4x).cos(6x).cos(8x).cos(10x) then, find the limit of {1 - [f(x)]^3}/[5(sinx)^2] as x tends to 0 (zero).
y = 100 - 4x ( a ) Find the value of y when x = 20.
-5
8x+30=4x+18 -4x -4x 4x+30=18 -30 -30 4x=-12 4x/4=-12/4 x=-3
d/dx[sin(4x)] = sin(4x) ======
yes
to find sin 35 here we take the angle = x=15 then 3x=45 , 4x=60 then 4x-3x=60-45 then by putting sin on rhs we will get cos 35 and sin 35 hope it helped you
if your by Lim's store, go right 4x and go down. there you have it!
-x*4*cos4x + (-1)*sin4x = -4xcos(4x) - sin(4x)
You would probably use a power-reduction trig identity to solve this equation. This states that sin2(x) = (1 - cos(2x))/2 Therefore, sin2(2x) = (1 - cos(4x))/2, or (1/2)(1 - cos(4x)) So, ∫ (1/2)(1 - cos(4x)) dx = (1/2) ∫ (1 - cos(4x)) dx. Then, ∫ (1-cos4x)dx = x - (1/4)sin(4x) + c Now, multiply that by (1/2) to get: (x - (sin(4x)/4) + c)/2 Since c is an arbitrary constant, we have: ½(x - sin(4x) / 4) + c OR 1/8 * (4x - sin(4x)) + c
y = -1 + 3 sin 4xLet's look at the equation of y = 3 sin 4x, which is of the form y = A sin Bx, wherethe amplitude = |A|, and the period = (2pi)/B.So that the amplitude of the graph of y = 3 sin 4x is |3| = 3, which tell us that the maximum value of y is 3 and the minimum value is -3, and the period is (2pi)/4 = pi/2, which tell us that each cycle is completed in pi/2 radians.The graph of y = -1 + 3 sin 4x has the same amplitude and period as y = 3 sin 4x, and translates the graph of y = 3 sin 4x one unit down, so that the maximum value of y becomes 2 and the minimum value becomes -4.
Once way is to plot it out, and note the intersection points. One spot is 0.2225400023465516 Follow the Wolfram|Alpha link for more answers.
(1/8)(x-sin 4x)
It is 9.1 inches (approx). L*[sin(x) + sin(2x) + sin(3x) +sin(4x)] = 28 inches where x = 360/10 = 36 degrees. Since x = 36 deg, sin(x) = sin(4x) and sin(2x) = sin(3x) So L*[2sin(x) + 2sin(2x)] = 28 inches L*[sin(x) + sin(2x)] = 14 inches L* 1.539 = 14 approx so that L = 9.098 inches or 9.1 inches, approx.
f(x) = sin(sin(x)). We don't really care about the 'x' or the '4x' or even the 'abs'. If we're looking at sin(sin(anything)), the greatest value the inside sine can have is 1, and the outer sine can't be greater than the Sin(1) which is roughly 0.8415.(assuming we're talking radians).
2(4x + 4) = (4x - 12) 8x + 8 = 4x - 12 8x - 4x + 8 = 4x - 4x - 12 4x + 8 = -12 4x + 8 - 8 = -12 - 8 4x = -20 4x/4 = -20/4 x = -5