Find the n-th power of 3 times the limit of sin (the nth power of X / 3), and n tends to infinity

Find the n-th power of 3 times the limit of sin (the nth power of X / 3), and n tends to infinity

The original formula = (x times sin (the nth power of X / 3)) / (the nth power of X / 3) = X. the limit sign is added after the equal sign

The denominator is SiNx, and the numerator is sin (the third power of x). X approaches the limit of 0

lim(x->0)[sin(x^3)/(sinx)^3]
=lim(x->0)[sin(x^3)/x^3]*lim(x->0)[x/sinx]^3
=1*1^3=1.

Find limit, 2's x power * sin (1 / 2 x power) x trend and infinite. Process

If x → positive infinity, (1 / 2) ^ x → 0
lim2^xsin(1/2)^x=lim{[sin(1/2)^x]/(1/2)^x}=1
The equivalent infinitesimal Sina ~ A is used, where a is an infinitesimal
If x → negative infinity, 2 ^ x → 0
lim2^xsin(1/2)^x=0
The product of infinitesimal and bounded variable is used as infinitesimal

Calculate: (X-Y) to the nth power - (Y-X) to the nth power (n is a positive integer)

N is odd
The nth power of (X-Y) - (Y-X)
=The nth power of (X-Y) + the nth power of (X-Y)
=The nth power of 2 (X-Y)
N is even
The nth power of (X-Y) - (Y-X)
=The nth power of (X-Y) - (X-Y)
=0

The fourth power of [2n power of (x + y)] and 2n + 1 power of (X-Y) (n is a positive integer) The fourth power of [2n power of (x + y)] and 2n + 1 power of (X-Y) (n is a positive integer)

The fourth power of [2n power of (x + y)] and 2n + 1 power of (X-Y)
=The 8N power of (x + y) is the 2n + 1 power of (X-Y)
=The [8N - (2n + 1)] power of (x + y)
=The 6n-1 power of (x + y)

When m, n are positive integers, the m power of a is x the n power of A When M. n is a positive integer, the m power of a and the n power of XA are equal to ()

When m.n is a positive integer, the m power of a and the nth power of XA are equal to (M + n) power of a)
＝＝＝＝＝＝＝＝＝＝＝
When multiplied by the power of the same base number, the base number remains unchanged and the exponent is added
That is: A ^ m × a ^ n = a ^ (M + n)
If we divide the same base power, the base number remains unchanged and the exponent subtracts
That is, a ^ m △ a ^ n = a ^ (m-n)
＝＝＝＝＝＝＝＝＝＝＝
The sign ^ denotes the power of a, a ^ m denotes the power of a, and others are similar

The degree of m power of polynomial x + n power of Y + m + n power of 2 [M, n are all positive integers] is

If M ≥ n, then the degree is m
If M ≤ n, then the number is n

Given that m and N are positive integers, and M > N, what is the number of times that the m power of x minus the n power of Y and the M + n power of 8?

M times
The M + n degree of 8 is a constant term, not a polynomial degree, so only x ^ m and Y ^ n are considered
Because m > N, it is m times

If the nth power of x = 3 and the nth power of y = 5, what are the values of (XY) to the nth power and (x? Y? 3) to the nth power (0.25) × (- 4) = ()

The nth power of (XY) = the nth power of X × the nth power of y = 15
The nth power of (x? Y? 3) is the nth power of (x ^ 2 × y ^ 2 × y) = (XY) × the nth power of y = 15 * 5 = 1125
The 2003 power of (0.25) × (- 4) to the 2004 power = (1 / 4) to the 2003 power × (- 4) to the 2004 power = - 2003 power of (4) × (- 4) to the 2004 power = 4 to the - 2003 power × (- 4) to the 2004 power = - 4 to the 2003 power X (- 1) = - 4

If the nth power of x = 2 and the nth power of y = 3, then the 3N power of (XY) =?

The 3N power of (XY)
=(the nth power of X and the nth power of Y)
=（2x3）³
=6³
=216