A meter reports the voltage of a circuit as R(t) = (t² - 4)/(t - 2) millivolts (mV), where t is the…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A meter reports the voltage of a circuit as millivolts (mV), where is the time in seconds. The meter fails at exactly s, so the formula gives no reading there. A technician wants to know what the reading would have been. Find the readings at s and at s. Then find the value that the readings approach as tends to s.
Need a reminder? The key ideaShow
A limit looks at the values of near , never at itself. The limit exists when the left-hand and right-hand limits are equal. For a polynomial, the limit at is its value at .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. in mV, for s.
Plan. Cancel the factor , then substitute.
Step 1. Cancel. For , .
Step 2. The two readings. At s the reading is . At s it is .
Step 3. The limit. As from either side, .
Check. The readings and lie on the two sides of and come closer to it as comes closer to s.
Answer: the readings are and , and they approach .
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