For which values of x will the rational expression below be equal to zero? (X-1)(x+5)/(x-5)
2 answers:
ANSWER
EXPLANATION
The given rational expression is
For the given rational function to be zero, then the numerator must be equal to zero.
We now equate the numerator to zero and solve for x.
This implies that,
We use the zero product property to obtain,
Hence the zeros of the given rational function are x=-5,x=1
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a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is
b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so
c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so
Then by linearity, we have