Step 1: Graph the Area (using Desmos): This confirms that we are dealing with a negative area under the x-axis. In other to get a positive value we have to put a negative sign in front of the integral: In other words, you’re taking the negative of the integral solution (a negativ...
So the solution is just as we’d expect from the graph: the limit is 0 as x approaches 3 from the left. Limit of Functions: Limit from Below Limit from Below, also known as a limit from the left, is a number that the “x” values approach as you move from left to right on the...
You can also simply graph the polynomial and make a visual judgement. In the image below, the polynomial has a relative maxima at 2 and relative minima at 4 and -2. The relative minima at -2 is also a global minima; the absolute maxima doesn’t exist because the value of the polynomia...
Step 3:Evaluate bnto see if it decreasing. One way to do this is to graph the function (I usedDesmos.com): Clearly, the function (and therefore the sequence) is decreasing and thelimitas n→∞ is 0. Therefore, this series converges. Proof of Dirchlet’s Test Watch the following video...