By Dawkins P.
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Extra info for Calculus I
F ( 0 ) = 1 . The function will always take the value of 1 at x = 0 . 2. f ( x ) ≠ 0 . An exponential function will never be zero. 3. f ( x ) > 0 . An exponential function is always positive. 4. The previous two properties can be summarized by saying that the range of an exponential function is ( 0, ∞ ) . 5. The domain of an exponential function is ( −∞, ∞ ) . In other words, you can plug every x into an exponential function. 6. If 0 < b < 1 then, a. f ( x ) → 0 as x → ∞ b. f ( x ) → ∞ as x → −∞ 7.
Now, one more time just make sure this is clear. Be forewarned, everything in most calculus classes will be done in radians! Let’s next take a look at one of the most overlooked ideas from a trig class. The unit circle is one of the more useful tools to come out of a trig class. Unfortunately, most people don’t learn it as well as they should in their trig class. Below is the unit circle with just the first quadrant filled in. The way the unit circle works is to draw a line from the center of the circle outwards corresponding to a given angle.
Let’s no work a couple of examples that involve other trig functions to see how they work. Example 5 Solve 9sin ( 2 x ) = −5cos( 2 x ) on[-10,0]. Solution At first glance this problem seems to be at odds with the sentence preceding the example. However, it really isn’t. First, when we have more than one trig function in an equation we need a way to get equations that only involve one trig function. There are many ways of doing this that depend on the type of equation we’re starting with. In this case we can simply divide both sides by a cosine and we’ll get a single tangent in the equation.
Calculus I by Dawkins P.