Q// Sketch the region of integration and evaluate the integral +/y+4 dxdy y+4

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Q: A Norman window consists of a rectangle surmounted by a semicircle. If the perimeter of a Norman win...

A: we should find the height of the rectangle such that the window will admit the most light.

Q: A company produces computers. The demand equation for this computer is given by p(q) = - 5q + 6000. ...

A: We have t find the number of units that needs to be produced for making the marginal revenue zero.

Q: The graph of f', the derivative of f, is shown below. Determine all possible inferences that can be ...

A:   ---------------------------------------------------------------------------- Key points: If f'x  ...

Q: Given the function f(x) = 2x + 16x° + 36x, determine all intervals on which f is both increasing and...

A: f(x) is both increasing and concave up in interval from 0 to infinity...as I have done solution in d...

Q: 25. Evaluate the following definite integrals. c) LIVII – x dx

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Q: S Vx + 3(x + 1)dx

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

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Q: %3D %3D a. m 1 b. mZ2 X C. mZ3 P. T

A: Given: 1. PT is tangent. 2. mMXP⏜ = 186°3. mNP⏜    = 90° 4. Point 'O' is a center of the circle.  -...

Q: 5] Sketch the graph of r(t) direction of increasing t. (sin t, 2 cos t) and show the %3D

A: Given: r(t) = (sint, 2cost)

Q: The integral represents the volume of a solid. Describe the solid. sin(x) dx O The integral describe...

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Q: ITEMS: Evaluate the following integrals. 1. / e* cos(2x) dx

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Q: 14. Evaluate the following limits. (3-x+x2, 5x+1Y e) lim 2x y-0+ 5x-7 lim 2 f) X0o ( 3x2 x sin x lim...

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Q: Find the Taylor polynomials of orders n = 0,1,2,3 , and 4 about x = xo, and then find the nth Taylor...

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Q: First make a substitution and then use integration by parts to evaluate the integral 6 cos (Vx) dx.

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Q: Evaluate the iterated integral | (a+ 2y) dyda. Give your answer correct to 2 decimal places.

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Q: x3 , which Consider the plane region bounded by the curves y? intersects at point (0,0) and (1,1) Fi...

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Q: 2dt (t – 3)vt² – 6t +5

A: Given: I=∫2dtt-3t2-6t+5   ...1   As we know that; ∫11+x2dx=tan-1x+C    

Q: 3. S sin(3x) cos(5x) dx

A: To evaluate: I=∫sin (3x) cos (5x) dx

Q: ·를 sin' X V cos x

A: This question is related to definite integration, we will solve it using given information. 

Q: Use cylindrical shells to find the volume V of the solid. The solid torus (the donut-shaped solid sh...

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Q: If you integrate the below integral successively for FIVE TIMES, how many terms including the C will...

A: ∫exdx1.Integrate with respect to xex+C12.Integrate with respect to x∫(ex+C1)dx=ex+C1x+C23.Integrate ...

Q: Alice rents a place in Cornelia Street and saw a paper on her desk. It says, "The product of two pos...

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Q: 36. Adams's Magic Hexagon. In 1957, Clifford W. Adams discovered a magic hexagon in which the sum of...

A: Note: As per our company's guidelines we are supposed to answer the first question only. Kindly aks ...

Q: use Substitution method to Schve (3メ -2Y +1)dx -(X-2Y-3)dy=o

A: Given:   3x-2y+1dx-x-2y-3dy=0

Q: 6. Given the space curve r(t) = (t, 2et, e2t), find the tangential and normal components of accelera...

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Q: For the following composite function, find an inner function u = g(x) and an outer function y =f (u)...

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Q: Given that (-1, 3) is a stationary point of the function f (x, y) = -x3 + x2 + 2xy+ y² – x – 4y. | D...

A: Given; fx,y=-x3+x2+2xy+y2-x-4y And The stationary point is: x,y=-1,3   We know that; If rt-s2>0, ...

Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places acc...

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Q: 2. 3. yo. %3D CX %3D

A: Let's find. 

Q: Question 6 Consider the function below: sin(x²+y) { (x, y) # (0,0) (x, y) = (0,0) f(æ, y) y-x Find t...

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Q: Use the trapezoidal rule with n = 5 to approximate %3D 5 cos(x) -d.x 1 Keep at least 2 decimal place...

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Q: (2+ In²x) dx J x(1 - In x)

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Q: (2x -y+2)dy + (x-2y +4)dx =D0

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Q: If someone could explain how this equation could be turned into a word problem? Example of the equa...

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Q: 23. Find the point c that satisfies the mean value theorem for integrals on the interval [1,4] for f...

A: The given function is: f(X)=2x2-7x, [1,4]

Q: B. (P +Q+R+M+ N) u= V4 - Vw +1 du Pw + Qw² +3 +R/w +1 u" or dw? 9u" (w +1)"

A: Given

Q: Find the limit of the function along the path y = 0. X-m lim (х.у) - (0,0) у -п C. -" 772 772 A. 0 В...

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Q: 3. Given r(t) = e' sin t i + et cos tj + v2e'k, a) find the arc length function for the curve measur...

A: We have to find arc length function, point and re-parametric equation. 

Q: Use the trapezoidal rule with n = 5 to approximate cos(a) - d.x Keep at least 2 decimal places accur...

A: ∫15cos(x)xdx ; n=5

Q: .3 dx J Tx²+9 .2

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Q: 2. Parabolic tangents and peculiar perpendicularities! a. Let la and lo be tangent lines to the para...

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Q: Use the price-demand equation below to find E(p), the elasticity of demand. x = f(p) = 12,500 – 325p...

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Q: Question 5 dy in terms of x. de 5. Given that y =u² - 4 and u=x +1, find dy dy du hint du de d du dx...

A: Topic:- derivatives   

Q: tate the domain and range of the following functions. y = 5x – 4 y = V - x {(x, y)ly = Vx2 – 16 %3D

A: Given problem is :

Q: Find the critical points c that correspond to local minima. (Use symbolic notation and fractions whe...

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Q: sec x dx 2. Vcot x

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Q: What trigonometric substitution will you use in solving the below integral? Note: Let W be the angle...

A: Put 8x=15tanw =[12×(15/8)³tan³w]/[5×15√1+tan²w] =(79.10/75)×(sin³w/cos³w)/[sec²w] =1.05sin³w/cos²w

Q: For the vector-valued function r, carry out the following steps. a. Evaluate lim r(t) and lim r(t), ...

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Q: Given the function f(x) = x° + 5x*, determine all intervals on which f is both increasing and concav...

A: Given :f(x)=x5+5x4To find: All intervals on which f is both increasing and concave up.