1 Partial Fraction Decomposition Find the partial frac- uon uecomposition of the rational function. 2 2x 13. 14. (x – 1)(x + 1) (x – 1)(x + 1) x + 6 16. x(x + 3) 5 15. (x - 1)(x + 4) 12 x- 12 18. x* - 4x 17. x* - 9 4 2r + 1 19. x - 4 20. x* +x - 2

Q: A rational expression f(x) has a patial fraction expansion of the form A В + 2а +7 (2æ + 7)2 where A…

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Q: 2x+8x Graph the rational function h (x) = x²- 6x+8 www 12+ 10 9. -12-10 -2 10 -6 -4 -2 -4 -8-…

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Q: x-4 x²+2x-15 Inx+51-Inx-31+ C 8 Option 1 S: dx 1 (x + 5)⁹1 Je In + C + x-3 -100 1 9 In|x + 5|ln|x −…

A: We can find the answer as below

Q: EXAMPLE 1 Investigating the Behavior of a Rational Function The graph of f(x) 1 is given. Complete…

A: The given rational function is f(x)=1x2

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Q: 4-The rational function y=ax?/(bx2+(2b+1)x +b) has one vertical asymptote and passes through point…

A: Solution

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Q: 15-20. Graphing rational functions Use the guidelines of this section to make a complete graph of f.…

A: Given the rational functions We need to graph the above rational functions.

Q: Number of relative extrema for polynomials  y=x2-2x y=x4-9x y=0.2x(x-1)(x-3)(x+2)(x+4)

A: The number of relative extrema is atmost one less than the degree of the given polynomial To find…

Q: find the limit of rational function (a) as x→0 and (b) as x→ -o. 5x8 – 2x3 + 9 h(x) 3 + x – 4x5

A: [a]limx→∞5x8−2x3+9−4x5+x+3 Therefore, limx→∞5x8−2x3+9−4x5+x+3=∞

Q: Match the rational functions to the graphs 3+# (1)(2)-27 (11)/(*)-3³-12 am (ir) 3r-4 (IV)/(x)-F 2²…

A: Graph : for vertical asymptote equate denominator to zero one vertical asymptote at x = 3  Hence ,…

Q: 2. The graph shoes the rational function f(x) along with its horizontal and vertical asymptotes, x =…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 6 pc Let f(x) = x3 + x+4 and g(x) = 2x + 3 in z,[x]. Then, upon dividing f(x) by g(x), we get O The…

A: Solution is given by long division of polynomial in Z7

Q: /3x² – 3x + 1 lim 1– 2x x--00 V3 does not exist 3 2 -V3 ||

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Q: #20

A: To determine the vertical asymptotes.

Q: limy- 3 3+ 3x – 18x 2 x-9

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Q: Let r(x)=p(x)/q(x) be the rational function graphed below, where p and q are polynomials that have…

A: First of all, consider the given condition for the rational function r (x). There are no common…

Q: lim h-0 (z+h)² +4(x+h)-²-4x h A B x³ + x4 x² + 4x 2x + 4 is

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Q: R(x) = x+3 / x(x+7)   Weite the ficen function as a single rational expression.  Find the…

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Q: (g) Use long division to find a polynomial P(x) that has the same end behavior as t(x). O P(x) = -x2…

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Q: x2-2x+2 -dx. (x-1)(x-2)² Jse the method of partial fractions and simplify your answer.

A: Given :  Integral   ∫x2 - 2x + 2(x-1)(x-2)2 dx    To find : Given integral by using partial…

Q: Consider the following rational function: g(x) (2x-6) x+8 1. Identify the vertical asymptote. 2.…

A: topic - rational functions

Q: A rational function is the function that can be written as the ratio of two polynomials. Rational…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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A: Let's find.

Q: Find all rational zeros and factor f(x). f(x) 3 6х3 + 19х2 +8х-5 5 1 О А. - 1, 2 3 : (х) 3 (x+1)(3х-…

A: here we have

Q: 9. Find the vertical asymptote(s). (x + 1)(x – 7)(x +10) f(x) (2 – 1)(21 – 7)(x + 10) O * = -10 O 0…

A: Here, the given function is: f(x)=(x+1)(x-7)(x+10)(x-1)(x-7)(x+10)

Q: 4 -2 -2 -4 7. Write the formula of the function f(x) whose graph is shown. 1(x) =+3 x-1 1(x) =- 3 -3…

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Q: 2.x(x+3)(x– 2) 5. Sketch the rational function f(x)= and state the following features listed below.…

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