Recall that
which means
Now, could be positive or negative, which means
. If we specifically knew the sign of
was positive, then we can simplify and write
or if it's negative,
The line plot shows the number of hours students studied for a final exam. A number line with one x above .5, one x above 1.5, o
2 answers:
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Answer:
Balloon made by Randi's sister
Balloon made by Randi
Step-by-step explanation:
Let Randi's sister made balloons.
Balloons made by Randi
total ballons
cast of
ballon
Cost of balloons
Given total money made
ballon made by Randi's sister
Ballon made by Randi's =
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:
