Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (Enter your answers using interval notation. If the answer cannot be expressed as an interval, enter EMPTY or Ø.) increasing decreasing f(x) = 7 x-9

Q: he given curve is rotated about the y-axis. Find the area of the resulting surface. y =  1 3x3/2,…

A: Given

Q: 43. y = (2+x)√2+(2-x)², [0,2]

A: Given function:- y=2+x2+2-x2

Q: The total cost (in hundreds of dollars) to produce x units of perfume is C(x) = 9x - 4 8x + 5 (a)…

A: The solution is shown below-

Q: Determine if the series O n=1 n cos (n) 3+n³ converges or diverges and choose the option that…

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Q: 3. Select the sine wave so the parent function is f(x) = sin (x). Start with a and b both set to 1.…

A: We have to draw the graph of sine wave with the changing values of b.

Q: Find the exact absolute maximum and absolute minimum of h(t) = cos(2t) + √3 sin(2t) on [0,1]. Show…

A: h(t)=cos(2t)+3sin(2t)for critical points, put h'(t)=0d dt(sint)=costd dt(cost)=-sint

Q: Consider the following planes. -5x + y + z = 5 15x - 3y + 5z = 25 (a) Find the angle between the two…

A: Consider the following planes -5x+y+z=515x-3y+5z=25a To find the angle between the two planes.b To…

Q: The First Gate Upon arriving at the first gate, you ask your computer to translate the riddle.…

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Q: How do you find the absolute max and min for problem 45?

A: The given function is: y=x+x2-2x ;          0, 4

Q: What is the minimum value of f(x) = x^2 - 8 ln x   on the interval [1,5]

A: To determine the minimum value of fx=x2-8 lnx on the interval 1, 5.

Q: Use the root test to determine convergence or divergence of the series of the series. n=1 3n¹3+n…

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Q: Consider the following equations. f(x) = √x + 5 g(x) x+5 Sketch the region bounded by the graphs of…

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Q: Differentiate. y' = y sec(0) tan(0)

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Q: 1 3 I(t) = ²/³ - 5 ² + 3 2 +86 (0 ≤ t ≤ 10)

A: I(t)=13t3-52t2+86for critical numbers put I'(t)=0d dt(tn)=ntn-1d dt(constant)=0

Q: 6. Evaluate the limit: lim x+-5+ a. 25 b. 2.5 5x X+ 5* C. c. -25 -co d.

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Q: Determine if the series O O A n = 1 ² n2 +4 5 n2 + converges or diverges and choose the option that…

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Q: Evaluate the Limits: a) limt->-1(t2+3t+2)/(t2-t-2) b) limx->9 (9x-x2)/(3-x1/2) c) limx->-inf…

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Q: From the graphs of f and g in the figure, we find the following. (Assume that each point lies on the…

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Q: 30. Given g(x) = 4x² + 1, use the difference quotient to find the instantaneous rate of change when…

A: Given function:- gx=4x2+1

Q: 3. Use the Root Test or the Ratio Test to determine whether the series is absolutely convergent,…

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Q: Use linear approximation, i.e. the tangent line, to approximate √16.2 as follows: Let f(x)=√x. Find…

A: Given: f(x)=x at x=16

Q: given by C(x) = -0.07x² + 75x. Find C(288) C(287) Interpret the result

A: we will find the required.

Q: determine if the mean value theorem can be applied to the function f (x)=x^2 on the closed interval…

A: we have given function f(x)=x2 which is continuous on the interval [3,9]. differentiation of this…

Q: Evaluate the double integral 10. Answer: 10ry dA, where D is the triangular region with vertices (0,…

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Q: JS₂² A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and…

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Q: Find a plane through the points (-2,6,6), (4,4,5), (2,-4,1) Calculator

A: Given :The points (-2,6,6), (4,4,5),(2,-4,1)

Q: 3. Use the limit definition of the derivative to find f'(x) for f(x) = 7x² + x.

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Q: The passcode for this gate is found by determining the domain of the derivative of f(x) and 45 then…

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Q: Find the Maclaurin series and find the interval on which the expansion is valid. f(x) = ln (1-x²)

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Q: After walking through the fifth gate, your computer informs you that more than half of the gates…

A: Given function f( t ) = 1a( 2t3 - 15t2 + 45 )

Q: Find the distance between the skew lines: x = 2 + 6t, y = 1+ 2t, z = 1 - 4t x = 3-t, y = 9, 2 = 4 +…

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Q: use differentials to approximate the vaule of sqrt(25.1)  A. 5.0300 B. 5.0200 C. 5.0100 D.…

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Q: (b) g(x) = (x + e*)², [0, In 4]

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Q: Find f'(x) and f"(x). f'(x) = f"(x) = f(x) = (x³ + 6)ex

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Q: 10. The average rate of change of f(x)= x² + x over the interval 0 ≤ x ≤ 4 is a. 20 b. 4 c. 5 d. 1

A: f(x)=x2+xinterval is  0≤x≤4formula for average rate of change is favg=f(b)-f(a)b-a

Q: Consider the center of mass of the following. A lamina occupies the part of the disk x² + y² ≤ 9 in…

A: The solution is shown below- As per company guidelines only first three parts are allowed to solve.…

Q: Graphs of the position functions of two particles are shown, where t is measured in sec notation.)…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt…

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Q: Convert the integral to polar coordinates and evaluate it (use t for 8): With a = √4 ²0b=0c and d=…

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Q: Find all Singular points of the given differential equation then classify as Irregular Singular…

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Q: Show that the substitution v= ax + by + c transforms the differential equation A first-order…

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Q: Find the arc length of the curve y = ln x - ²² on the interval [1,3].

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Q: Find the inflection points of f(x) = x¹ + 9x³ — 15x² + 15. (

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Q: Find the volume of the region bounded above by the paraboloid z = x² + y² and below by the triangle…

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Q: Find the general solution for the differential equation. dv 6- - 12xy - x = 0 y = = 1/2 + Ce=x² y =…

A: Given differential equation:- 6dydx-12xy-x=0

Q: 5. Find the points on the graph of f(x) = x³ - 3x where the tangent line has slope 0.

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Q: Find the Cartesian equations a. r = 3 b. rsin 0-10 c. rcos 0+3=0

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Q: 6. What principal invested at 13% compounded continuously for 6 years will yield $9000? Round the…

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Q: Refer to the following figure, which displays a right circular cone along with the formulas for the…

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Q: Suppose a product's revenue function is given by -8q² + 800q, where R(q) is in dollars and q is the…

A: The given revenue is Rq=-8q2+800q, where Rq is in dollars and q is the number of units sold. To find…