Hey guys I need some help with this question so if anyone could help that would be great THANK YOU!!
1 answer:
The left hand derivative of the given function comes out to be 3a² + 3ah + h².
Deducing the Left Derivative:
The given function is,
f(x) = x³ + 2
⇒ f(a) = a³ + 2
The left hand limit is the definition of the left-hand derivative of f: f′⁻(x) = f(x+h)f(x)h. F is said to be left-hand differentiable at x if the left-hand derivative exists.
Now, the formula for the left derivative of a function is given as,
f'(a)⁻ = [ f(a+h) - f(a) ] / [ (a+h) - a]
f'(a)⁻ = [ ((a+h)³ + 2) - (a³+2) ] / h
f'(a)⁻ = (a³ + 3a²h + 3ah² + h³ + 2 - a³ - 2) / h
f'(a)⁻ = (3a²h + 3ah² + h³) / h
f'(a)⁻ = h(3a² + 3ah + h²) / h
f'(a)⁻ = 3a² + 3ah + h²
Hence, the left derivative is 3a² + 3ah + h².
Learn more about derivative here:
#SPJ1
You might be interested in
Answer:
With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is of at least 216.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error:
For this problem, we have that:
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is
We need a sample size of at least n, in which n is found M = 0.04.
With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is of at least 216.