Find div F and curl F if F(x, y, z) = 9e"Y i – 2 cos yj+ 7 sin? z k. div F= curl F=

Q: 5. This problem will walk you through using integration to find the formula for an area of a circle:…

A: equation of circle  x^2+y^2=1 y^2=1-x^2 y=±1-x2 according to question circle lies only 1 quadrant so…

Q: X1 + 2x2 + x3 = 12 X1 – 2x2 + x3 = 0 X1 + x2 – x3 = -1 Solve the following system using Gauss-…

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Q: Find V· (V × F), if F(x, y, z) = e®²i+ 4xe®j – 5eV²k. V.(V × F) =

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Q: Q2 (a) Let n E N and let ở, w e R". Show that if ở · w = 0, then || ở + w||2 = || ||² + ||w||². (b)…

A: This question can be solved using the concept of dot product of two vectors.

Q: The graphs of f(x) and g(x) are shown. For what values of x does f(x) = g(x)? x = -2, x = 0, x = 3…

A: We have to choose correct option

Q: 1. The approximate value of -31.8 using linear approximation O -2.0025 O None of the choices O…

A: Ni

Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: Find V. (V × F), if F(x, y, z) = 3e²*i+9xe*j – 4ev*k V· (V × F) =|

A: Use the curl and divergence for the F.

Q: 1- x2 If f(x) = then f'(x) = x² + 1 2/x(x² + 1)³

A: Given : f(x)=xx2+1   To Show: f'(x)=1-x22x(x2+1)3

Q: Which identity is most useful in evaluating sin² x dx? sin? x + cos? x = 1 cos 2x x = 1- 2sin? O…

A: The given integral,         ∫sin2x dx

Q: S (1/(X(Im)*) dx X(Inx)

A: LetI=∫1xlnx2dxLet u=ln(x)differentiate 1xdx=duI=∫1xlnx2dx.I=∫1u2du.I=∫u-2duUse power…

Q: Evaluate the definite integral. 1+eJ+/k]di i-ej+ k o ? - 1 1 + (-" – 1) j + k e-1)1- (e - 1) J+ k o…

A: Given: I=∫01e9ti+e-tj+tkdt As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫eax+bdx=1aeax+b+C

Q: Q1) Determine if the following integrals converge or diverge. If the integral converges determine…

A: Given query is to find integral converges or diverges.

Q: 1. For the autonomous differential equation = y(4 – y²) find the equi- librium solutions and…

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Q: 1- r 3 Consider the lines l : 2 2 - y = z +1 and l2: = y –2= 3 1. Determine a direction vectors for…

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Q: Problem No. 1: Evaluate - dx using basic substitution method.

A: First I have used the substitution to make integral easy and then evaluate it.

Q: Determine the radius and interval of convergence of the following power series. The radius of…

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Q: 3. S- dx 1-sin'x

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Q: ㅇ z"+ 35 to

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Q: Use the formula k(t) = |r(t) × r"(t)|| ||r(t)||° to find «(t). r(t) = 8 cos(7t)i+ 8 sin(7t)j + 3tk…

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Q: 3 to dy 2 +Sinx COSX

A: Given query is to find the solution of the differential equation.

Q: : Consider the differential equation xy" + 3xy – 3y = 3x2 – 2x. %3D = x -3 (a) Verify that y1 = x…

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Q: J4-yズ ニo dy

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 3yz²k; (2,…

A: This question is based on divergence of vector.

Q: 8 tan¬1 n 1 + n² 00

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Q: tan 0 d 30. dO sec² y dy

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Q: 11. Rules of Definite Integrals: If f(x)dx =12, S" S(x)dx = 6, and "S(x)dx= 4 , find the following:…

A: We need to perform integral.

Q: Consider h(x, Y, z) = cos (xy) + eY% + ln (xz). Determine the directional derivative of h at the…

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Q: All edges of a cube are expanding at a rate of 3 cm per second. How fast is the volume changing when…

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Q: Find r'(t). r(t) = (tan(10t))i+t cos(t)j – VEk NOTE: Enter your answer in terms of i, j, and k.…

A: Given problem :- r(t) =(tan-1(10t)) i+t cos(t) j-√tk Find:- r'(t)

Q: Question 8 of 10 View Policies Current Attempt in Progress Find r'(t). r(t) = (tan(9t))i+t cos(t)j…

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Q: Find curl (3zi + 4xj+ 5yk). curl(3z i+ 4xj+ 5yk) = ( i )i + ( i )j + ( i )k

A: We will find the curl.

Q: ) (2xy+y2) dx - 2x2 dy = o 2) xy dx-(x + zy)? dy = o メ+ 2y)? dy

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Q: If y = x2 is expressed with parametric equations such that = 6 when x = 1, what is ? dt dx %3D dt

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Q: Cives f(x.g) = メー2メラーリメy+5 Find the Ccritical points oo f and all detevmine the nature of each of…

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Q: What isfor the curve given by x = (t – 1)³ and y = vt ? | dx 1 2VE 6VE(t-1)2 3(t-1)2 O Option 4…

A: Using chain rule of differentiation

Q: (-5 S + (0.9)" | lim

A: Given query is to find the value of the indicated expression.

Q: dt 1-cos t+sin t

A: First we shall simplify the expression then integrate

Q: Determine the vector field of F. F(1, y) = 9i – 3j

A: kindly attached following graph.

Q: 2- Sinx-y cos?x =.

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Q: (D² +1)y = sec x. %3D

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Q: dx Half-angle Substitution cos x +sin x-1

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Q: S(cosh4x + sinh2x)dx

A: Given: ∫cosh4x+sinh2xdx

Q: Consider the following. 3x - y + z = 6 Sketch a graph of the plane.. y -6 y -4 2 y 4. 2 2. Label any…

A: Given :3x-y+z=6To find it's intercept

Q: x+1 8. -dx (x-1)

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Evaluate the definite integral. i-ej+ k 7 O el - 1 7. O el - 1 i+ (e- - 1) j+ k i- (e-- 1) j+ k O e…

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Q: r(t) = 4 cos(7t)i+4sin(7t)j+3tk

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Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). 13 9ts r(t) = e"i+etj K(t) :

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Q: Evaluate the area of the region bounded by y2 = x and y2 = 6−x.

A: To find : Area between y2=x and y2=6-x First let's find the intersection points x=6-x⇒x=3 Therefore,…

Q: Find the conservative vector field for the potential function by finding its gradient. g(r, y, :) +

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