simulation: https://www.geogebra.org/m/mztyxd5b
12:14 PM Fri Sep 4 @ 76% webassign.net Use the & slider to choose some value of & greater than zero. As you do, two parallel blue lines will appear, producing the interval (L - &, L + 8) where L is the value of the function at a (represented by the horizontal black line passing through the dot). Use the & slider next to choose some value of o greater than zero. You will see two vertical lines appear, one a distance o to the right of the dot and the other a distance S to the left of the dot. Now find a value of 8 such that for x-values between the vertical lines, the y-values are between the blue lines (in other words, the curve should enter and exit the box formed by the lines through the sides rather than through the top or bottom). When you have found such a value of o, the shading within the box will turn green (otherwise, it will be red). This is one possible value of o for the precise definition of the limit for the given value of & and the selected function. You can click the Zoom In button to get a better look and to set a more precise value of o. To explore limits at infinity, choose Limits at Infinity from the drop down menu in the upper left corner. Then choose a function from the drop down menu in the upper right corner. In order to choose the limit of the function at infinity, slide the Xmax slider to the right to see what value the function eventually approaches. Then use the L slider to adjust the horizontal line. If the function simply levels off, align the horizontal line with the right end of the function's graph. If the function oscillates, try to move the horizontal line to the center of the oscillations at the right end of the function's graph. Use the & slider to choose some value of & greater than zero. As you do, two parallel blue lines will appear, producing the interval (L - &, L + 8) where L is the limit at infinity (represented by the horizontal line). Use the / slider next to choose some value of N. You will see a vertical line appear. Continue to slide the / slider to the right until you find a value of / such that all values to the right are between the blue lines. When you have found such a value of /, the shading within the box will turn green (otherwise, it will be red). This is one possible value of / for the precise definition of the limit for the given value of & and the selected function. You can click the Zoom In button to get a better look and to set a more precise value for N. + Simulation - Exercise Select the second function in "The Limit of a Function", y = V x. (a) Set a = 5 and & = 0.2. Use the o-slider to find a value for o so that f(x) is within 0.2 of f(5) for all values of x where 5 -8
