Two numbers have a sum of 72. What is their product if it is a maximum? (A) 1296 B) 1297 c) 1298 1269

Q: Find V· (V × F) if F(x, y, z) = 4 sin ci + 7 cos(9x – 10y)j + 10zk. V · (V × F) =

A: Given F(x,y,z)=4sinx i+7cos(9x-10y) j+10z kTo find∇·(∇×F) first we need to find ∇×Fwe know that ∇×F…

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Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 6xyz k. V × (V × F) =

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Q: Find V · (V × F) if F(x, y, z) = 3 sin xi + 6 cos(6x – 7y)j + 3zk.

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Q: Evaluate the following improper integrals. Tell whether it is convergent or divergent. dx

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = ellti+etj K(t) ||

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Q: The most conveneient way to evaluate x2- by substitution is to let Vx2- 4 =y A True B) False

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Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

A: The solution is given below.

Q: (a) / Which of the following integrals is equal to -2+ In 2? X - 4 dx (a) 4- I dx (b) 2 - 4 da (c),…

A: To find which of the given integrals has given value

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Q: Q2/ Check the symmetry of r² = -sin(20) %3D Ans./ Symmetry about the origin

A: Symmetry

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Q: Question 2 Find the inverse Laplace transform of H(s) - (;+)-

A: H(s)=1s2-e-s1s2+2s+e-4s4s3+1s L-1{H(s)}=L-11s2-e-s1s2+2s+e-4s4s3+1s…

Q: The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. Use inear…

A: Given problems:- 1).    The circumference of a sphere was measured to be 76 cm with a possible error…

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A: This question can be easily calculated by applying the concept of motion of particle in a magnetic…

Q: Consider the quadratic function g(x)=x²-4x+36. Define a new function S(x) by S(x)=the slope of the…

A: As per our norms we have to write three multiple questions at a time kindly repost remaining…

Q: 2. Give the domains for the following functions where: 1 f (x) = and g(x) = V4 – x 1 (i) (ƒ og)(x)…

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Q: 1. Solve for x, if 0 < 0 < 2n. Write your answers in exact values only. 2 2cos" x + cos x- 1 0

A: Given: 2cos2x+cosx-1=0  and 0≤θ≤2πlet cosx=mthen 2cos2x+cosx-1=0        2m2+m-1=0We know that root…

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Q: Find div F and curl F if F(x,y, z) = x°i – 11j + yzk. - div F= curl F=

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Q: Evaluate the integral (12x + 6y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: 3. For the given differential equation xy' – 4y = x*e* a) Find P(x) and Q(x) functions of a FOLDE.…

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Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

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Q: PART III: APPLICATION 5. a and b have magnitudes of 5 and 6, respectively. The angle between them is…

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Q: EXAMPLE 6 Evaluate the following integral. tan (r) dr SOLUTION First we write tangent in terms of…

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Q: Suppose a product's revenue function is given by R(g) is units sold. 5g? + 500g, where R(g) is in…

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Q: y = (sinh(@)) Solve for y'. Express your answer by factoring out a common facto

A: First I have taken the log on both side to the given function and then differentiating it with…

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Q: Find the integral. 4 9) x4 In 2x dx A) 391.74 B) -202

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Q: Find the area of the surface generated by revolving the curve about each given axis. *- 7t, y= st,…

A: Surface area genarated by revolving the curve about x-axis is parametric notion is…

Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (9t + 4)i + tj, 0 sts1

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Q: Find all values of the angle 0 (in radians, with 0 s 0 < 2n) for which the matrix cos e -sin 0 A =…

A: The solution is given below

Q: A ball is kicked such that its height (h) can be represented by the equation h = - 16t2 + 64t + 9,…

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Q: Find the limit. lim (t i – 3 j+ t?² k) t-2 lim (t i- 3 j+1? k) = j + i i+ i i k

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Q: Given: y = arctan sinh find y' at x 2 cosh 1 3(1+sinh 1) cosh 1 Oy = 1+sinh 1 cosh 1 1+sinh 1 %3D…

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Q: Evaluate (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (5, -5)

A: The objective of the question is evaluate the definite integral.

Q: 2. sin 2wcos 2wchw

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Q: Find the volume of the solid that results when the region bounded by x=y^2 and x=4y+5 is revolved…

A: Given: To obtain the volume of the solid when the region bounded by x=y2 and x=4y+5 is revolved…

Q: 5. [sin-' x dx Ans. x sin'x - V1-x² +

A: We will use integral by parts to evaluate integration of arc sinx

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Q: Find the arc length of the graph of r(t) eV2li +e¬V2lj+2tk, 0<t< v2 ln 9 NOTE: Enter the exact…

A: Given problem:-

Q: 2. Integrals containing sin u cos v can be solve using identity. (a) Double-angle (b) Half-angle (c)…

A: Let's find.