Find the particular solution determined by the initial condition. f'(x) = 3x273 - 6x; f(1) = - 7 f(x) =

Q: Find the volume x=y-y2; x=0 revolving at y-axis

A: Given problem:- Find the volume x=y-y2 ; x=0 revolving at y-axis

Q: Evaluate the following integral using trigonometric substitution. хах а. Vx2– x – 1

A: To evaluate the following integral using trigonometric substitution.∫x dxx2-x-1

Q: Find the volume of the solid of revolution if a quarter of an ellipse in the first quadrant with…

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Q: Determine if the following statement is true or false. The points P1(12, 9, 7), P2(6, 4, 0), P3(0, –…

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Q: Find * 4xe²? dx. e2z² + 2ez² +2 -2tan-1(e*² + 1) + c 2tan-1(e* + 1) + c O Option 2 Option 1…

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Q: Find the Fourier series of f(x) as given over one period and sketch f(x) and partial sums: (0 if –2…

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Q: Given the graph of y=f(x) below, at which of the marked x-values can the following statements be…

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Q: Find the center (h, k) and the radius r of the circle 4x2 + x + 4y? + y – 10 = 0.

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (– 10,…

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Q: АCTIVITY GIVEN : 2x 2x 1 2х + 3 1 f (x) = 1 –x 8 g(x) = 3(x + + 4 h(x) = 6 a.lim -4 · f (x) d.lim (8…

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Q: find of the f llowing 2. 2 -5x*

A: Solution of question is written in below steps.

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

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Q: 4. Use the definition of derivative to compute the derivative of the following functions at x 1: a.…

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Q: f k车9. if D < X< 1. if 1大メ$4. if X7 4, 3-X X-3 IS the Functibn 9(x) Continuous on |I4 ? Un (-∞ 8,0)?…

A: check contineous between [1,4] g(x) = 3 - x2 between 1 to 4 check for 1+ and 1- for 1- g(x) = 3…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

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Q: find the parametric equations of the line through (-3,0,2) that is parallel to 3i-4j+k. x(t)= y(t)=…

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Q: Given the plane i = (-2, 1,5) + s(3, -2,0) + t(1, 1, 5), s,t € R. The plane cuts the x, y and z-axes…

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Q: Draw a function f(x), defined for all real numbers x, with one local maximum and two local minimum.

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: To use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

Q: Explain why S is not a basis for M, O sis inearly dependent. O s does not span M.2 O sis linearly…

A: We can solve this as follows:

Q: Finding a Limit In Exercises 11-28, find the limit. Use a graphing utility to verify your result.…

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Q: 13 dt 9+6t 4 (9+6t)5

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Q: Let D be the tetrahedron in the first octant bounded by the coordinate planes and the plane 6x + 3y…

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Q: Evaluate the limit below. - 2x2 + 13x – 21 lim x→3 х — 3 -

A: limx→3-2x2+13x-21x-3apply L hospital rulelimx→3-2(2)x+131limx→3-4x+13

Q: dy +y = y² sin x dx

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Q: Select the response that best describes the phase relationship between v1(t) and i (t). Vi(t) =…

A: Follow the procedure given below.

Q: Finding Vertical Asymptotes In Exercises 63–68, find any vertical asymptotes of the graph of the…

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Q: Find the area bounded by the curves y=8x-x2 and y=x2, and the line 4x-y=-12.

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

Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

A: Here, note that any plane through the point P(14,-12,7) is of the form:…

Q: Find the mode.   51​, 44​, 49​, 48​, 51​, 33​

A: Given  51, 44, 49, 48,51,33

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: This question can be solved using the concept of equation of line in 3D geometry.

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: In dx

A: Given: I=∫lnxx2dx   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: 1. Given: x(x+8)(x – 2) (x+ 2)³ 8(7x – 4) (x+2)ª ° f(x) = (x+ 2)² ' and f"(x) = with f'(x) = d.…

A: Function is undefined at x= -2   Interval f' (-∞, -8) +ve -8 0 (-8, -2) -ve (-2, 0) +ve…

Q: Consider the following. u = 5i + 4j, v = 31 + 2j (a) Find the projection of u onto v. 33 3i + 2j 13…

A: u = 5i +4j v= 3i+2j   a projection of u onto v  = (u*v)v/|v|2 u*v = 15 +8 =23 |v|2 = (32+22)2 = 13…

Q: (6) At the start, an experiment records 1 gram of bacterial culture, and the culture's weight is…

A: Given: The initial amount of bacteria i.e. at t=0 hours = 1gm The culture's weight carrying capacity…

Q: In x 35. lim

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Q: 7. Approximate (22 + 3) dz using four rectangles and the left endpoint method.

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Q: The graph of a function f(x) is shown below. If the definite integral | f(2)dz gives the area of the…

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

Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). v= (4, 5) a = 3 b = 1

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Q: 2x+ln x

A: We know that power rule of derivatives is  d(xn)/dx = nxn-1.     Here i attached the solution of…

Q: (5* )csch x²+1 dy if Find dx 1. (a) y = x >0. (ecosh 5x) In Vx +1 )

A: Find your answer below

Q: Find the angle 0 between the vectors in radians and in degrees. - co) + sin() = cos 4 u = cos i +…

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Q: Find the exact length of the polar curve r = 2+2 cos 0 . Show All Your Work!

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Q: X1 – 4x, + X3 = 2 4x1 + X2 =1 Xz + 4x3 =-1

A: Since the question is asked to solve by two different method solution by one of the method is given…

Q: MY NOTES ASK YOUR TEACHER Consider the following functions. f,(x) = 4, f,(x) = cos2(x), f,(x) =…

A: Let's find.

Q: Answer the following about the function F(x)=x^4-24x^2+700. Justify all your answers. A. Find all…

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Q: Finding a Limit Graphically In Exercises 5 and 6, use the graph to find the limit (if it exists). If…

A: f(t)=ln(t+2)t At some point t=a we say that limit exists if both  right and left side limits exist…

Q: Units

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Q: 1 Sava (x³/3=1)/x dx (Hint : let x = u°)

A: Solution of question is written in below steps.