.
Difficulty Rating: 
Source: Calculus, by Roland Larson,6
ed., p. 77.
Find the constant a such that the function f is continuous on the entire real line if
.
Difficulty Rating:
Source: Calculus, by Roland Larson,6
ed., p. 77.
We don't want there to be a break in the graph at x = 0, so the second rule (which is linear) must pick up exactly where (what height) the first rule left off. So, we determine where the first rule was heading by taking the limit as x approaches zero, and get
Solution:When we plug in zero (into the bottom rule according to the function's design), it needs to begin at that height, so we plug in 0 for x and set its height equal to 4, and we get the solution for a: .
.
Calculus II (BC): Polar EquationsProve that the distance between polar coordinates
and
is given by the polar distance formula
.
Difficulty Rating:
Solution:Begin with the rectangular distance formula, and then substitute in our famous translation formulas for x and y as follows:
The trick in the last step is to recognize the cosine difference formula from Trig. For some reason the scripts are fuzzy. Sorry about that.
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