Tutor profile: Nicole B.
Determine the limit as x approaches -1 of (x^2+3x+2)/(x^2-1).
To find the limit, we substitute the x-value into the function. When we substitute -1 into (x^2+3x+2)/(x^2-1), we get 0/0 which is indeterminant. This indicates that there is a removable discontinuity at x=-1. We will need to simplify our function prior to substituting -1 in. (x^2+3x+2)/(x^2-1)=(x+1)(x+2)/(x+1)(x-1) which reduces to (x+2)/(x-1). Now when we substitute x=-1 into (x+2)/(x-1) we get 1/-2. Thus the limit as x approaches -1 of (x^2+3x+2)/(x^2-1) is -1/2
Determine what is 20% of 300.
To determine percentages of numbers, we will multiply the percent by the number. So 20% of 300 will be determined by doing 20% times 300. We will need to convert the 20% to a decimal. Percent means per one hundred. Thus 20% is 20/100 which is 0.20. Multiplying 0.20 times 300 results in 60. 60 is 20% of 300.
Determine the equation of line passing through the points (2, 3) and (7, -1).
To find the equation of a line given two points, we'll first need to find the slope for those points. Using the slope formula, we get the slope of m= -4/5. Now that we have the slope and a point, we can use the point-slope form of a linear equation. The point-slope form is y-y_1=m(x-x_1). We can use either point for (x_1, y_1). Our equation would be y-3=-4/5(x-2)
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