Use Lagrange multipliers to find a vector in 3-space whose length is 4/3 and whose components have the largest possible sum. (x, y, z) = ( i i

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Evaluate the limit below. Inx4 lim

A: Given: limx→∞lnx4x3   As we know that; The Power law: ddxxn=nxn-1 And From the property of the…

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

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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: 10. * -1 x CSc

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Q: 2. Apply Maclaurin's series to obtain the first 5 terms in the series for e ,

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Q: 2)tind the third degree Taylor polynomial Is (x) centered at a= I forr the function f (x)= 2

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Q: Evaluate the definite integral. (Use symbolic notation and fractions where needed.) 12 dt 3t +4

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Q: If f (x,y) = In(x² + y²), then fx(x,y) + fyy(x, y) is: а. 0 x+y b. x2+y2 2х+2у с. x²+y2 d. Undefined

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Q: esin 2x [In (cos 2a)]? 2esin 2( cos 2x In (cos 2x) + 2 tan 2] 2esin 2a (cos 2x ln (cos 2x) + 2 tan…

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Q: Σ E n=2 n·ln(n)

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Q: The percentage of P doctors who accept a new medicine is given by P(t)=100(1-e^-0.16t) Where t=time…

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Q: 1 Given Perimeter of a rectangle is 130ft Find length and width which will give Maximum Area

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Q: Find the points on the ellipse 5x2 + y2 = 5 that are farthest away from the point (1, 0). smaller…

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Q: Integration of (Sin(x) + Cos(x))e^x is_

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Q: The plane with normal vector (0, – 2, – 4) containing the point (-7,4,-3) has equation Aæ + By + Cz…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: A company determines that its weekly online sales, S(t), in dollars, t weeks after online sales…

A: S(t)=300etAverage weekly sales =13-0∫03300etdt                                 =13300(e3-e0)…

Q: Consider the planes x – 10y – 2z = 3 and 2x – y + z =-13. Find the following. 1. The cosine of the…

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Q: Evaluate the limit below. 36 – x2 - 6 lim 5x

A: We have to evaluate the limit                                                limx→036-x2-65x

Q: Find the tangent plane to the equation z = - 2a2 – 3y? + 5y at the point (– 4, 4, – 60) | Z = 16x…

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Q: Consider the triangle shown in the figure. Let A = 11 and B = 5 (in feet) and the angle 1 = radians.…

A: Consider the triangle shown in the figure. Let A=11, B=5 in feet and the angle t=π4 radians. To…

Q: Find the net area and the area of the region bounded by y 2cosx and the x-axis between x = - and x =…

A: Use the integration to find the net area and area bounded by the given region.

Q: The value of the integral 1 2 x²y° dy dx is: 2..3 1

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Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x2 for -2 sxs…

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Q: Use x = au, y = bv to show that the area of the ellipse x2 y? = 1 is rab. 62 a2

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Q: Compute the value of the following improper integral. If it is divergent, type "Diverges" or "D".…

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Q: 7. The function f (x,y,z) = xyz, when subject to the constraint x + 2y + 3z = 72, has one critical…

A: 7. The function f(x, y, z) = xyz, when subject to the constraint x + 2y + 3z = 72, has one critical…

Q: Simplify (x) and find any vertical asymptotes. x²_ 4 f (x)= x+ 2

A: Vertical asymptote of the rational function f(x)=p(x)q(x)is given  q(x)=0

Q: In 6 19) ex dx In 3

A: ∫ ex dx = ex +C

Q: Draw a function F(x), defined for all real numbers x, that satisfies the following properties.…

A: The first derivative is everywhere positive and the second derivative is everywhere negative

Q: sinh x 1+ cosh x

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Q: 4x-x dx x2-x-30 x³-x

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Q: Evaluate the limit below. 28 – 4x + 7x2 lim -9x² – 4 - 4

A: LetL=limx→∞ 28-4x+7x2-9x2-4Divide N and D by x2L=limx→∞ 28x2-4xx2+7x2x2-9x2x2-4x2L=limx→∞…

Q: Given –6i is a root, determine all other roots of f(x) = x + 2x² + 36x +72. x= -6, ±2i x = -2, +6 x…

A: Given query is to find the other two roots.

Q: x-2ax+a If lim exists, then a = 1-x a -1 b 1

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Q: Consider the following. u = -6i - 4j – 2k, v = 4j + 4k (a) Find the projection of u onto v. (b)…

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Q: Question 1 Consider the following IVP: x" - 4x' + 4x 4e2, x(0) = -1, x'(0) = -4 Find the general…

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

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

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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: Find the area of the portion of the surface z=f(x,y) = x^2+ y^2 that lies below the plane z = 9.

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Q: dx 6. S; ezx+1

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Q: Find the total mass of the wire with density p whose shape is modeled by r. r(t) = t'i + 2tj + tk,…

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Q: 2) Calculate each of the limits by considering logarithm of the limit first. a) lim x'n x x→0+ b)…

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Q: Find the particular solution of the differential equation as determined by the initial condition. dB…

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Q: one-sided limit (if it exists). 72. lim

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Q: Differentiate y=x^lnx

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Q: Find k if the shortest distance from (-2,5) to the circle x2+y2+kx+4y=12 is 3.6 units. a) 5 b) 6…

A: Find K.

Q: 1. fx³e*/2dx /4 2. S*x sin 2x dx

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Q: 1. Evaluate the limit below. -3(x – 10) lim x→10 x2 – 100

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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