A school sold small and large boxes of fruit for a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Anoth
2 answers:
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We can model the problem in many different ways.
One example is to divide 12 counters (modelled as circles) into six boxes (modelled as square)
We have two circles inside each box
The model is shown in diagram below
One example is to divide 12 counters (modelled as circles) into six boxes (modelled as square)
We have two circles inside each box
The model is shown in diagram below
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:
