The easiest way to find such limits, where there is a numerator and a denominator is to apply <span><span>Hospital's Rule.
1st find the derivative of the numerator and the derivative of the denominator, if it still gives an indeterminate value, find the second derivative of N and D
3) lim sin(2x)/x when x →0
Derivative sin2x → 2cos2x
Derivative x→ 1
2cos2x/1 when x→0 , 2cos2x → 2
and lim sin(2x)/x when x →0 is 2
4) lim(sinx)/(2x²-x)
→cosx/(2x-1) when x →0 cosx/(2x-1) = -1
and lim(sinx)/(2x²-x) when x →0 is -1
and so on and so forth. Try to continue following the same principle
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1/3 chance. You have 15 marbles 5 which are black. That makes it 5/15 which reduced would be 1/3
If we know that 180-5=128 that means that that equation must be equal to 128.
(2^3x+1)=128
By putting 128 into exponential form with a base of 2 you get 2^7:
(2^3x+1)=2^7
Since these have the same bases we can set the exponents equal to 7. This will give us an exponent of 3x+1=7. By Subtracting across and dividing by 3 you get:
3x=6 to 3/3x = 6/2
This gives us a final answer of:
x=2
