One diet uses a ratio of 9:5:4 for carbohydrates, protein, and fat. A nutritionist is developing a diet that provides 450 calori
2 answers:
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Answer: 2.093
Step-by-step explanation:
As per give , we have
Sample size : n= 20
Degree of freedom : df= n-1=19
Significance level :
Since , the sample size is small (n<30) so we use t-test.
For confidence interval , we find two-tailed test value.
Using students's t-critical value table,
Critical t-value :
Thus, the critical value for the 95% confidence interval = 2.093
If we evaluate the function at infinity, we can immediately see that:
Therefore, we must perform an algebraic manipulation in order to get rid of the indeterminacy.
We can solve this limit in two ways.
<h3>Way 1:</h3>By comparison of infinities:
We first expand the binomial squared, so we get
Note that in the numerator we get x⁴ while in the denominator we get x³ as the highest degree terms. Therefore, the degree of the numerator is greater and the limit will be \infty. Recall that when the degree of the numerator is greater, then the limit is \infty if the terms of greater degree have the same sign.
<h3>Way 2</h3>Dividing numerator and denominator by the term of highest degree:
Note that, in general, 1/0 is an indeterminate form. However, we are computing a limit when x →∞, and both the numerator and denominator are positive as x grows, so we can conclude that the limit will be ∞.