The Area bounded by the parabola ay=x^2, the x-axis, and the line x=b is revolved about the x-axis, Find the volume genertated.

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A: Given query is to find the area under the curve

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A: From graph, it is clearlimx→∞cos1x =limx→-∞cos1x = 1

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A: Solution :- By compare standard cosine function y= Acos(Bx-C)+D

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A: Given problem:-

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Q: 5. Lim xsinx x-0+

A: Let A=limx->0+xsin x

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Q: In problems 5 and 6 find the particular solutions of the given differential equations. d²y dy +9y =…

A: To find the solution of the given differential equation.

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A: This question is related to rate of change, we will solve it using given information.

Q: 6. Find the area bounded by the curve y = log x, the x-axis, and the line x = 2.

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Q: x²y" + 2xy' 6y = 0 -

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Q: Find the gradient of f(x,y,z) = (x² + y² +z²) Vf|(1,2,2) = Oi+Dj+Ok (Type integers or simplified…

A: ∇f(x,y,z) = ∂∂xi+∂∂yj+∂∂zkf(x,y,z)

Q: 5. Lim xsinx x+0+

A: Consider F=limx->0+xsin x Taking logarithm on both sides

Q: 4. Find 3x 2t dx/e²t dt

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Q: cscxdx 5+ cos²x sin²x

A: solution:-∫csc25+cos2xsin2xdx,    {…

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

Q: 3. Reverse the order of integration in 24e² dydx and then evaluate the integral with the new limits

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Q: Find the interval of convergence for The interval of convergence is a E n=1 (x − 2)" - n² 2n

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Q: √3.01³ +2.992

A: We need to evaluate :

Q: numerate and explain each briefly the six guidelines in solving maxima/minima problems

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: Find the volume of the region bounded above by the plane f(x,y) = 2x + 5y + 6 and below by the…

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Q: Write an equation for the transformed logarithm shown below 5 4 3 2 1 -5 -4 -3 -2 -1 3 4 5 f(x) = N…

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Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x+2y=5.

A: Given Function f f(x,y)=14-x2-y2 on line x+2y=5We need to find the maximum value For the line…

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A: We can find the answer as below.

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A: Given: ∫01∫0z2∫03y2sinz6dxdydz

Q: Л ST 6 77 6 EN F/3 2 3 -0 i 11 6 4) V3 2² 2 27 3 F|N 11 6

A:

Q: Find the length of the arc of a circle of diameter 8 meters sub tended by a central angle 2pi/3…

A: Let "θ" be a central angle in a circle of radius "r". Let "s" be the length of the arc cut off by…

Q: Find the parallel projection of the vector v = onto the vector w=.

A: Given problem:- Find the parallel projection of the vector v=&lt;4, -5, 7&gt; onto the vector…

Q: 4) Determine the value of the 4) -2 6)-1 c) o d) 1 I'm 10,0 хсу e) DNE xy 2x² √x² + y²

A: If the function approach the same value k along any path into (0,0) then the limit is k. If two…

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)=3 ex cos (yz), Po(0,0,0),…

A: Solution: f(x,y,z) =3exCos(yz) P0=(0,0,0)

Q: ·Sa 20. x² dx (x − 1)(x² + 2x + 1)

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Q: A person starts walking from home and walks: 2 miles East 2 miles Southeast 5 miles South 2 miles…

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Q: Question 4 A 3 2 1 2 3 4 To find the blue shaded area above, we would calculate: [ f(x) dx = area…

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Q: Find an equation for the plane that is tangent to the surface z = In (x+y) at the point P(0,1,0).…

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Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: II. Solve the following problems. Enclose final answer. 10. At what rate is the vertex angle of a…

A: Given:-radius of right circular cone, r=3 ftaltitude of right circular cone, h=4 ftaltitude is…

Q: Set up the definite integral required to find the area of the region between the graph of y 19-2 y =…

A: We have to find out area

Q: Find an equation of the tangent line to the graph of the equation 6x - 5x8y7 = 36e6y at the point…

A: In this question, we will compute the equation of the tangent line of the given curve.

Q: Determine the angle, to the nearest degree, between the vectors= (4,6,-2) and y = (1,8,2)

A: Solution is done in step 2

Q: Find f'(-2) if f(x) = 3 -7x. f'(-2)= (Simplify your answer. Type an integer or a fraction.)

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Q: 5) Write the equation of the line through the points P(1,3,7) and Q(2,5,11) in: a) Vector form b)…

A: topic - equation of line through two points

Q: the sum if convergent. 4) 2-6+18-54...

A: In this question, we will evaluate this series and test for convergence.

Q: Question 16 Find e > 0 such that the area of the region enclosed by the parabolas y = 2²-² and…

A: Given problem:- Find c&gt; 0 such that the area of the region enclosed by the parabolas y = c2 -x2…

Q: 6) Write an equation of the plane through the points P(5,3,8), Q(6,4,9), and R(3,3,3).

A: The plane passing through the points P5,3,8, Q6,4,9 and R3,3,3

Q: Find the slope of the tangent line to the graph of the given function at the given value of x. y =…

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