1. A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 18 inches wide by turning up one-third of the width on each side. What width across the top will give the greatest cross-sectional area?

Q: (e* + y)dx + ( 2+ x+ ye' )dy =0

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Q: All functions with trigonometric functions are integrable

A: Given All functions with trigonometric functions are integrable. 

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A: Let's find. 

Q: , find the partial derivatives.

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A: Find derivative using product rule and composition of functions rule

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A: We draw the graph step by step . For the graph we use different colours which represents the various...

Q: 1. .f(x) = [(x² – 9)Vx + 2]°

A: As per our guidelines we are supposed to answer only one question.kindly repost other question as a ...

Q: Find the MacLaurin series of f(x) = sinh(3x) . Express your answer in the form Σan (x - c)^n. The pr...

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Q: Compute the partial sums S2, S4, and S6 of 1 1 + • 6 1 1 + 8 · 10 + + 2. 6 · 8 (Use symbolic notatio...

A: The given series,    12.4+14.6+16.8+18.10+......

Q: sin ()-/9 – a² – a V9 - ? +C 81 O sin () -av9- a + V9 – a² + C 0-sin-1 (즐) - 응2V9-2 +23v9-27 + C ○ 뽑...

A: Given: The integral is ∫ x29-x2 dx

Q: whether

A: As per policy, only first question is answered. Please refer to the image below 

Q: dz du Evaluate the integral Jo 5 the concept J + c. 2zv9z2-4 using uvu?-a? arcsec a a

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Q: Determine which of the following are ordinary differential equations and which are partial different...

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Q: C. Solve the initial value problem: 2xydx + (2y² – 3x²)dy; y(0) = –1.

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

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Q: Find the minimum point for the curve y = x- 4x -1.

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Q: On a circle with a circumference of 38 cm, the arc intercepted an 100° central angle. Find the arc l...

A: Given : circle with a circumference of 38 cm the arc intercepted an 100° central angle

Q: 3x+4 lim 2e x→-1

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Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 1 where the tangent line is horizontal. (х, у) %3...

A: Solution ) given f(x) = y = 2x3 + 3x2 - 12x + 1 f'(x) = 2 × 3 × x3 - 1 + 3 × 2 × x2 - 1 - 12 + 0 For...

Q: solve

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Q: y' – 5y = x²e* – xe5x |

A: As per our guideline we are supposed to be answer only one question you can repost other questions i...

Q: boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on...

A: topic - application of derivatives

Q: If F is a continuous on the set of real numbers, then (A True (B False

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Q: tc os4e d E |- cos 40

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Q: For the Polynomial POX)= ²-2x-1Bx-10: 2. :) List all f the possible values of Zeros for Pa), accordi...

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Q: Find the tangent line to the curve y = 2x - x? at (2,0)

A: We can find the required answer as below

Q: 2.

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Q: At sues pizza they sell a large pizza for $8.25 and charge $1.50 for each topping. write an equation...

A: We can find and justify the answer as below.

Q: From the top of a lighthouse 96 feet high, the angle of depression to a small boat is 37.1658°. How ...

A: Follow the procedure given below.

Q: Test the series below for convergence using the Ratio Test. 97 n! n=1 The limit of the ratio test si...

A: This question is related to limits,  we will solve it using given information 

Q: Find the equation of the tangent line and normal line to the following curves at the indicated point...

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Q: Find the intervals where the function y=f(x)y=f(x), whose graph is given below, is increasing and wh...

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Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT. 1...

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Q: day tidket for a for children as least G than 13 years old, A day tickei for Students at least 3 tha...

A: f(x) is the cost of ticket (in dollar) and x is the age of children (in years). x is the input and f...

Q: Calculate the integral: dx J (e² – 4)(e* + 6)

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Q: 13: 3. y = V(4x + 3)3

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Q: 20 15- 10- 5- 10 15 20 The rate at which people arrive at a theater box office is modeled by the fun...

A: In order to find the number of people entered in the time 0 < t < 20, we need to obtain the ar...

Q: &r4- V Let y=f (x) + C be the antiderivative of F (x) = determine the value of C (use 3 decimal plac...

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Q: x + 3x – 1 lim V4r6 – 2x エ→ーx 2.r

A: We have to find limit

Q: Let f be the function given by f (x) = sin(2x) cos(1 +x). What is the average value of fon the close...

A: Given function f(x)=sin(2x) cos(1+x)       ; 1≤x≤3 use the formula 2 sin A cos B = sin(A+B)+sin(A-B)

Q: Find an equation of the tangent line to the curve y = x/x that is parallel to the line y = 6 + 3x. y...

A: The given question has been solved in detail

Q: Find f'(x). f(x) = e – x³ arctan(x) -(3 + 3x2 arctan(x) + arctan(x)(3x4)) x2 +1 f'(x)

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Q: (0, 1) (0,0) (1,0) FIGURE 0.1. The triangle T of the problem. Consider the triangle T with vertices ...

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Q: If we are told that f'(5) = 6 evaluate h'(0) where h(1) = f(5 cos r + x² + 2x).

A: Given function h(x)=f(5cosx+x7+2x)  

Q: d²y 1. 5 dx - 6y = 0 y(0) = 2; y'(0) = 4 - %| dx² d²x(t) 2. ·+ w?x(t) = 0 dt2 x(0) = A; x'(0) = vo %...

A: I am attaching image so that you understand each and every step.  

Q: 11. y x Sin x + (1 -x) Cos x Oa. x Sin x+ 2x Cos x b.x² Sin x ©* Sin x dxSin x+ 2 Sin x

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Q: e the ratio test to determine whether the series converges or diverges. If the test is inconclusive,...

A: Topic:- series convergence test

Q: 5. The depth of water in a port is modelled by the function d(t) = pcosqt + 7.5, for 0 <t < 12, wher...

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