I am studying for a Calculus test and have the answers for the study guide but I'm having trouble with problems 2, 3, 4 (finding
maximums and minimums for each) as well as #9 (computing the limit). The answers are written next to each question.
1 answer:
#2) Use quotient rule
Remember for solving log equations:
#3) Derivative of tan = sec^2 = 1/cos^2
Domain of tan is [-pi/2, pi/2], only consider x values in that domain.
#4 Use Quotient rule
#9 Use double angle identity for tan
This way you can rewrite tan(pi/2) in terms of tan(pi/4).
Next use L'hopitals rule, which says the limit of indeterminate form(0/0) equals limit of quotient of derivatives of top/bottom of fraction.
Take derivative of both top part and bottom part separately, then reevaluate the limit. <span />
Remember for solving log equations:
#3) Derivative of tan = sec^2 = 1/cos^2
Domain of tan is [-pi/2, pi/2], only consider x values in that domain.
#4 Use Quotient rule
#9 Use double angle identity for tan
This way you can rewrite tan(pi/2) in terms of tan(pi/4).
Next use L'hopitals rule, which says the limit of indeterminate form(0/0) equals limit of quotient of derivatives of top/bottom of fraction.
Take derivative of both top part and bottom part separately, then reevaluate the limit. <span />
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Answer:
Step-by-step explanation:
Given (64 y Superscript 100 Baseline) Superscript one-half.
Let us write it into an equation.
Apply radical rule: and
Hence, is equivalent to (64 y Superscript 100 Baseline) Superscript one-half.
Answer:
36.04% probability that at most two of them would read at less than 850 words per minute
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the binomial probability distribution.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Percentage of students who read less than 850 words per minute.
Pvalue of Z when X = 850. The mean is and the standard deviation is
has a pvalue of 0.3085.
30.85 of students read less than 850 words per minute.
If 10 students are selected at random, what is the probability that at most two of them would read at less than 850 words per minute
This is when
. So
36.04% probability that at most two of them would read at less than 850 words per minute