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Finding where certain functions are positive and negative plays a very important role in calculus. Find the intervals where each function is positive and the intervals where each is negative. Write your answers in interval notation. $$h(x)=x^{2}+9 x+2$$

Finding where certain functions are positive and negative plays a very important role in calculus. Find the intervals where each function is positive and the intervals where each is negative. Write your answers in interval notation. $$h(x)=x^{2}+9 x+2$$

Precalculus: Graphs and Models

Modeling with Linear and Quadratic…

Solving Inequalities

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ANSWERED

Tavis Lam verified

Numerade educator

QUESTION T - POINT Let \( R \), ce the requin bounded to the \( r \), hit thy the graph of \( x=\frac{\cos \left(9 y^{2}+1 i\right.}{9} \), to the left by the \( y \)-axis, and hetween the lities \( 32-\frac{4 x}{7} \) and \( y-\frac{11 \pi}{6} \). Lise the shell method to find the vulume of the solid of revo ution formed by revolving \( R \) about the \( x \) Fxx: Enre an exact value in terms of \( \pi \). Lo not inclukle units in your answer Proside your arswer below: \[ 6 x^{2}+\frac{2 x}{3} \]

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Tavis Lam verified

Numerade educator

QUESTION 13 + 1 POINT Determine if the area bounded by \( y>0, y \leq 1 /(\sqrt{1-3 x}) \), and \( x \leq 0 \), is firite or infinite. If the area is finite, find the area. Select the courct answer below: ? infinite ? 2,3 ? 5/3 ? 2 ? \( 2 / 3 \)

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Tavis Lam verified

Numerade educator

QUESTION 17 - 1 POINT Evaluate \( \int \sec ^{7} x d x \) using reduction formulas. Select the correct answer below: ? \( \frac{1}{6} \tan ^{5}(x) \sec (x)+\frac{5}{21} \tan ^{2}(x) \sec (x)+\frac{5}{16} \tan (x) \sec (x)+\frac{5}{16} \ln |\tan (x)+\sec (x)|+C \) ? \( \frac{1}{6} \sec ^{5}(x) \tan (x)+\frac{5}{24} \sec ^{3}(x) \tan (x)+\frac{5}{16} \sec (x) \tan (x)+\frac{5}{16} \ln |\sec (x)+\tan (x)|+C \) ? \( \frac{1}{6} \sec ^{5}(x) \tan (x)-\frac{1}{24} \sec ^{2}(x) \tan (x)-\frac{5}{16} \sec (x) \tan (x)-\frac{b}{16} \ln |\sec (x)-\tan (x)|+C \) ? \( \frac{1}{6} \tan ^{5}(x) \sec (x)+\frac{5}{24} \sec ^{3}(x) \tan (x)+\frac{5}{16} \sec (x) \tan (x)+\frac{5}{16} \ln |\sec (x)+\tan (x)|+C \) ? \( \frac{1}{4} \sec ^{4}(x) \tan (x)+\frac{5}{12} \sec ^{3}(x) \tan (x)+\frac{5}{12} \sec (x) \tan (x)+\frac{5}{16} \ln |\sec (x)+\tan (x)|+C \)

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ANSWERED

Tavis Lam verified

Numerade educator

QUESTION 16 , I POINT Calcuiate the area, in square units, bounded by \( g(x)-3 x+77 \) and \( f(x)=x^{2}+9 x+82 \) over the interval \( [-5,-1] \). Give your answer as a fraction, if necessary. Frovide your answer below: 1. Jiquenc worls

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ANSWERED

Tavis Lam verified

Numerade educator

QUESTION IS - 1 POINT Calcuate the areas, in square units, bounded by \( f(x)=6 x^{3}-16 x^{2} \quad 7 x \) and \( g(x)--7 x^{3} \quad 14 x^{2}+28 x \) nyer the interval \( (4,10) \). Fince your answer as an integer or simplifed kacton. Provide your arswar belson: \footnotetext{ \( \frac{1781}{4} \) Timense unia. }

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ANSWERED

Tavis Lam verified

Numerade educator

QUISTION : 14: - 1 POINT Consibur the curve \( C \) arlines to be \( f(x)-2 x+8 \) neer the interyal \( 0 \leq x \leq 4 \). What is the arciength or the curve \( C \) ? Gova ori exact answer: Provide your arswer below: \[ 4 \sqrt{ } 5 \]

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Tavis Lam verified

Numerade educator

QUESTION IS - I POINT The resultal slicine, through the center of the so id \( S \) is the base described by the ellipse \( \frac{x^{2}}{81} \quad \frac{y^{2}}{9}-1 \). Crass sections uf \( S \) perpendicilar to the \( z \)-axis and the ellipticul tama ancircles. What is the volume of \( S^{\prime} \) - Inter your answer in termis of \( \pi \). Provideyour ansoe below: 10sr I

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ANSWERED

Tavis Lam verified

Numerade educator

QUISTION V2 1 POINT Define \( R \) as the egion bounded hy the graphs of \( f(x)-2 \sqrt{x+6}, x=2, x=6 \), and the \( x \)-axis. Using the disk method, what is the vohme of the solid of revolution generated by rotating \( R \) about the \( x \)-axis? Enter your anwer in terms of \( \pi \), and do not include units. Privitise your answer beiow. nita

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ANSWERED

Tavis Lam verified

Numerade educator

QUESTION 11 , 1 POLM+ Determine the area, in stuare units ol the region bounsed above by \( f(x)-12 x-7 \) and below ty \( g(x)-5 x-4 \) over the Intervai 10,16]. Pavide your answe brlow: [528] square units

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ANSWERED

Tavis Lam verified

Numerade educator

QUESTION 10 • 1 POINT Find \( \int \frac{8 \ln x}{x^{4}} d x \) using integration by parts. Give only the function as your answer. Do not include " \( +C \) ". Provide your answer below: \[ -\frac{\ln x}{x^{2}}-\frac{1}{8 x^{8}} \]

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