Consider the graph and determine the open intervals on which the function is increasing and on which the function is decreasing. Enter Ø to indicate the interval is empty. Enable Zoom/Pan 10 -5

Q: Find the volume of the solid that results when the region enclosed by the given curves y = e-2, y =…

A: The given curves are; y=e-2x, y=0, x=0 and x=1 So, the bounded region is as shown below. Apply the…

Q: Determine whether the sequence is increasing, decreasing, or not monotonic. (Assume that n begins…

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Q: Given any second-order non-homogeneous differential equation, describe how you would decide between…

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Q: Prove the given identity. tan0 + cot0 = csc@sec®

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Q: 3. Find the point(s) on the graph of the curve fle)-+3+ where the tangent is horizontal.

A: To find the points on the graph of the curve fx=x33+3x+4x, where the tangent is horizontal.

Q: The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area…

A: let side of triangle = x    Given

Q: Find three positive numbers whose sum is 260 and whose product is a maximum. (Enter your answers as…

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Q: Use Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the…

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Q: Find an equation for the hyperbola that satisfies the given conditions. Vertices: (±1, 0),…

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Q: 5 | (2a3 + 5æ – 4) dæ

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Q: 19. Using the l'Hospital's rule to find the limits e3r – 1 In(ln æ) 1 e" – 1- x – ² (a) lim a→0 In(x…

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Q: 4. Find the integral of your answer in problems 2a and 2b. CO

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Q: Determine "k" so that the vectors 3a- 4b and 5a+ 2k b are collinear. Justify your response.

A: Topic = Vector

Q: Sketch the graph of f(x) sketching the graph of a function. Label your graph. = -3r – 4x² + 6x – 2…

A: Function

Q: (2x + 3)dx x² + 4x + 29

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Q: Find the area under the curve y=sin2x from x=0 to x=3pi/4 A. 2 B. 1/2 C. pi D. 3/2…

A: The curve y=sin2x from x=0 to x=3π4

Q: 13. A model used for the yield of an agricultural crop as a function of the nitrogen level in the…

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Q: Find the missing values assuming continuously compounded interest. (Round your answers to two…

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Q: f (x) = sec? x +1

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Q: 1 7. (x dy – y dx) = 0 x² + y?

A: We are given a differential equation  1/(x2+y2) ×(xdy - ydx ) =0 We have to determine whether it is…

Q: What is the approximate error in the volume and surface area of a cube of edge 2 feet if an error of…

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Q: 1. Find the moving trihedral and the curvature at any point of the curve R(t) = cost î + sint j + k.…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +7 1 (?, ?) lim t+\6t2 + 7'5t

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Q: FIND THE GIVEN DIFFERENTIAL EQUATION Homogeneous Equation ( 3x + 4y - 1) dx + (18 x + 24 y + 2) dy…

A: The given DE is: (3x+4y-7)dx+(18x+24y+2)dy=0⇒dydx=-3x+4y-718x+24y+2⇒dydx=-3x+4y-76(3x+4y)+2

Q: (2x + 6)dx x2 – 2x + 17

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Q: 1 Find Vf(P) and Df(P). (a) f(r,y, z) = y² + 2² – 4x2; U = i – +; P(-2,1,3) %3D |

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Q: a cost i 6. Find the moving trihedral and the curvature of R(t) a sin 2t k OE

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Q: Find the equation of the circle shown Ih

A: Three point  ( 0 , 4 ) , ( 0 , 2 ) and ( -2 , 0 )   equation of circle   From the graph  center ( h…

Q: de 1+sin e+ cose CO

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Q: onsider the following curve. y = x, 0sx<5 Set up an integral in terms of x that can be used to find…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A: Draw the region and use the washer method of finding the volume of revolution of solids.

Q: Evaluate the integral (2x + 6)dx x² – 2x + 17

A: Given ∫(2x+6)x2-2x+17dxTo evaluate integral:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Determine whether the sequence converges or diverges. If it converges, find the limit.

Q: 12. Given f (x) = x³ – 12x + 1 (a) Find the intervals on which f(x) is increasing or decreasing. (b)…

A: I have appended the formula used in the solution part.

Q: Sx°Inxdx

A: Given query is to find the value of the integral.

Q: 15. What would you choose for your u here if you used integration by parts? f 3t e2" dt а. t b. e21…

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Q: An equation of the tangent line to a curve at the point (3, 5) is y = x + 2. if at any point (x, y)…

A: To find the equation of curve

Q: Calculate

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Q: 5. Given y=af(1 Find when =1 if f(2) = tand f(2) = 5.

A: Topic = Derivative

Q: 8 sin z 6 sin z + 4 cos a Let f(x) = Then f (2) = The equation of the tangent line to y = f(x) at a…

A: Given: f(x)=8sin x6 sin x+4 cos x f'(x)=(6sin x+4cosx)d(8sin x)dx-(8sin x)d(6sin x+4cosx)dx(6sin…

Q: Evaluate the following integrals? .3 1)S x² e3* dx 2) S dx x²+25 dx 3) 6x – x2 4) | cos(In x) dx

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

Q: 2. Transform the polar equation into a Cartesian equation. 4 r = 4 + sin 0

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Q: da

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Q: Direction: Find the equation of the tangent lines. Show your solution. 1. f(x)= x2 +5x +1 at (6, -2)…

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Q: Find the cost function if the marginal cost function is given by C'(x)=x 1/2 + 5 and 9 units cost…

A: The marginal cost function is given by,   C'x=x12+5

Q: Rates of Change: Oscillating Spring At Answer the following question, and give a written…

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

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Q: Write 32/3 as an integral

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Q: 1 6. Find dx. V2x2 –8x+2

A: Solving

Q: Evaluate the integral. 1 (4 + r)3 dr

A: