Joaquin recorded a temperature of 62*F this morning for science class.The temperature increased 61/2*F In the afternoon before d
ecreasing 8.7*F in the evening. What was the temperature? Enter your answer in decimal form
1 answer:
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Answer:
Part 1)
See Below.
Part 2)
Step-by-step explanation:
Part 1)
The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:
We want to verify that the expression:
Is the linear approximation for the function:
At <em>x</em> = 0.
So, find f'(x). We can use the chain rule:
Simplify. Hence:
Then the slope of the linear approximation at <em>x</em> = 0 will be:
And the value of the function at <em>x</em> = 0 is:
Thus, the linear approximation will be:
Hence verified.
Part B)
We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.
In other words:
By definition:
Therefore:
We can solve this by using a graphing calculator. Please refer to the graph shown below.
We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.
In interval notation:
Answer:
Step-by-step explanation:
The first step is to combine the parts of the numerator and denominator into one rational expression each. Those will have the same denominator, so their ratio is the ratio of their numerators.
