Question 8 of 10 < > View Policies Current Attempt in Progress Find r'(t). r(t) = (tan(9t))i+t cos(t)j – vtk NOTE: Enter your answer in terms of i, j, and k. r'(t)

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Q: X+3 24) Find the integration by using: J: dx 2x3-8X

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Q: Apply different integration techniques in solving the integrals. - Properly carry out integration…

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

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Q: What is the area under the curve given the parametric equatio x = t3 and y = t° over [0,1]? O 1/8 O…

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Q: 2. S CoSx+sinx-1

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Q: Find div F and curl F if F(x, y; z) = x°i – 7j+yzk. div F= curl F=

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Q: Use the formula k(t) ||r(t) × r"(t)|| to find «(t). %3D r(t) = t²i + t°j K(t)

A: We have to find the value of k(t).

Q: iF Zz fexiy) where R= ě- ě Gud ge ě- ě show That!- +y5= (e-ぎ)( - 24

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Q: 4. S(9x + 33x +22) dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find V· (V x F) if F(x, y, z) = 2 sin xi + 2 cos(8x – 9y)j+ zk. - V · (V × F) :

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Q: 11. Let -4 А -4 -4 -3 -3 (a) (i) Show that -4 is an eigenvalue of A with corresponding eigenvector…

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines.

Q: S 2y(yª – 4)¯³ dy

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Q: A famous leaning tower was originally 184.5 feet high. At a distance of 130 feet from the base of…

A: Using sine rule, all parameters are evaluated.

Q: Evaluate the definite integral. e16t i + e¬tj +t k )dt O el6 – 1 (e-- - 1) + i+ (e-1 – 1) j + , k 16…

A: To solve the given integral.

Q: 10 dx 5. S (10 +1)5 6. S 2r(e**+1 – 2**) dx

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Q: Match each point in polar coordinates with either A, B, C, or D on the graph. D

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

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Q: Sx² sinh xdx

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Q: x² Consider the function f(x) = x² –1 (a) Find the intercepts of the graph of f (if any). (b) Find…

A: This is a problem related to function calculation. Based on the general formula and concept we will…

Q: 9. S (6eº+1)/½ eo 10. |(1 + 2x)³ dx

A: We can solve as follows

Q: Find V · (V × F), if F(x, y, z) = 3e*i+ 3xe"j – 8evk. - V ·(V × F)

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Q: 8 Evelluate the double integral: + 3x) dydx

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Q: Given z = f(а, у), а — г(и, v), у — у(и, v), with 2(0, 2) = 1 and y(0,2) 4, calculate z,u(0, 2) in…

A: We have to find the value of zu(0,2).

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

A: Given problem:-

Q: Solve the following second order homogeneous linear differential equation if the 4 initial…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: Find curl (8z i + 9x j + 10y k). curl(8z i + 9x j+ 10y k) Di +(i Dj +( )k

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Q: 8) Fiad the volume of the solid gonereted by revelving the regien beunded by tue graphs of equetians…

A: Given problem:- Find the volume of the solid generated by revolving the region bounded by the graphs…

Q: Find the maximum rate of change of f(z, y, z) = tan(6z + 2y + 3z) at the point ( – 1, 3, – 2).

A: We need to find maximum rate of change.

Q: dy Find of sin x + cos y = ety. dx

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Q: S V25 – 4x²

A: For the solution follow the next step.

Q: tan 0 d 30. dO sec² y dy

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Q: 1 Find the Fourier series for 1, if -п <х <0 { { -1, f (x) = -1, if 0 < x< n

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

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Q: (D2 – 1)y = 2e-*(1+e-2*)-2, %3D

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Q: Cives とz f(xy)= J36-9メ-す i) Find domajn and Ram ge Foy the fuclien

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Q: J4-yズ ニo dy

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Q: Suppose that f(z, y) = z*y°. The directional derivative of f(1, y) in the directional ( – 1, – 2)…

A: We can solve this as follows:

Q: Q1: Find dy/dx for the following functions:- (1) e – 3* = x sinh y (2) tan-12 = (Inx' + y²)

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Q: 2. A garden lot is bounded by the curves y = x and y = 9. If its area is in square meters and it…

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Q: х- у 3. f(x, y, z) = y? + а. f(3, —1, 2) b. d. f(2, 2, 100) с.

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Q: Find V x (V x F) If F(z,y.2) 10ryj+5zyzk. V x (V x F)

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Q: 1. (1 + y?)° dy 2. S sin x+cotx dx sin?x

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

A: Ni

Q: Evaluate the definite integral. ell! i + e¯'j + t k )dt O ell – 1 (e-1 – 1) - (ell – 1) i – (e-1 –…

A: The given integral is: I=∫01e11ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: Let A + 0 and ACB. Show that NB CNA.

A: Given :A≠∅A ⊆ B

Q: 3. fesec'e Vran e* + 2 dx

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Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A: Let's find.

Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.