y = x(x2 – 4)

Q: Evaluate the definite integral. ellt i+ej+t k)dt O ell – 1 (e – 1) + (ell – 1) i – (e-l – 1) j + k…

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Q: FiNd the volumes OF the solids gewerated by revolving +he regions bounded by the graphs oF the…

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Q: 2. S x²-6x-4 xp x+2

A: Given: I=∫x3-6x-4x+2dx As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫a·fxdx=a·∫fxdx

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

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Q: Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and passing…

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Q: 4. The voltage signal from a standard wall socket can be described by the equation V (t) = 325…

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Q: We want to fenca in a ne slide b up againd a lacae building and Idbesn't noedh fancing rechanguler…

A: This question can be solved using the concept of maxima or minima.

Q: 7. Interpretations of Inter a) Determine the position function, s(t), of an object if the…

A: a)

Q: A. Use polar coordinates to describe the region shown. 1.

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Q: Given function:  f(x) = 4x^3 - 7x^2 + 2x - 5 A. Find the exact x & y coordinates of stationary…

A: Given: f(x)=4x3-7x2+2x-5

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

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Q: Use the half-angle formulas to find the exact value of the trigonometric function sin 112.5°. ...…

A: Use the half-angle formulas to find the exact value of the trigonometric function sin 112.5°.

Q: Describe the graph of the equation. r =-18i+(1-j+:k O Itisa parabola in the plane: = -18, with…

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Q: Fnd the Indefinite Integral and check your result by differentlation. (Use C for the constant of…

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Q: D. Find the orthogonal trajectory f the family of curves y= x+h %3D

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Q: Find the volumes oF the solids geverated by revolving +he regions bounded by the graphs oF the…

A: Given:-  the region bounded by  y=2x2y=0  and x=2rotating about the x-axisusing washer/disk method…

Q: X+3 Q4) Find the integration by using: dx 2x3-8X

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Q: Consider the exact first order diff. equ: |M(x,y) = 2.xy- 3.x? N(x, y) = x² - 2y (I): (2xy - 3x )dx…

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Q: Find V x (V x F) if F(x, y, z) = 5xyj+7xyz k. %3D V × (V × F)

A: Curl vector

Q: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: x + 2y = 1 , x – 2y = 8 . Credit will be given for use of the method, and not for the so y =-7/4.

A: We will solve using cramers rule.

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

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Q: Which substitution is needed to evaluate the integral S tan* x sec² x dx =? u = tan* x, du = sec? x…

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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: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: 4 of 21 Which of the following is not an identity? I. tan z + cot z = sec z csc z II. cos? z = sin…

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Q: y = Vx + 3 from x=1 to x=4

A: We find the area under given curve and bounded by axis and given lines x=1 &amp; x=4 using definite…

Q: Find the value of the following definite integrals. Show your solution. 1. L* + 4) dx 2. f(cos x +…

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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: S tan -1x dx

A: Solution is done in step 2

Q: 5x3+4x2-5 dx

A: Use power rule integration technique

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

A:

Q: sin(6x) lim ? 2+0 sin(2x) Does not exist O 3

A: Given problem:-

Q: Use the formula k(t): |r'(t) × r"(t)|| to find k(t). r(t) = ti + t°j K(t) =

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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: sin() cos( 2

A: To Find :   ∫sinx2cos3x2dx   Note: 2sinAcosB=sin(A+B)+sin(A-B)

Q: - sin² ydy 6. 4 tan" y

A: As per the guidelines I can solve only first question

Q: OMMU a) Find the exact area of the shaded region. b) Use the calculator to approximate to the…

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Q: A curve in the plane is defined parametrically by the equations x = t +t and y t* + 2t2. An equation…

A: The equation of the tangent line is: y-y1=mx-x1 Where m is the slope of the tangent line. And The…

Q: 5. What is the general solution of the following differential equation ( .6³yod?y =0)? ,d*y +9. dx2…

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Q: Find r'(t). r(t) = (tan¬(2t))i+t cos(t)j – vtk NOTE: Enter your answer in terms of i, j, and k.…

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Q: dz Find given: dt z = ze", z = t°, y = 1+ 4t dz dt Your answer should only involve the variable t

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Q: Find V · (V × F) if F(x, y, z) = 2 sin xi+ 8 cos(4.x – 5y)j + 2zk. %3D - V·(V × F) = %3D

A: Given :F(x,y,z)=2 sin xi+8 cos(4x-5y)j+2zkTo find : ∇·(∇×F)

Q: Determine the vector field of F. F(x, y) = 6i – 3j

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Q: 1. Rules of LDef nite Integrals: 12 a) b) rpx 12 12 f(x)dr 4, find the If f(z)dr = 12, " $(z)dz = 6…

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Q: (tan x) dx

A: Given query is to find the integral.

Q: 7. Į V1- xdx 8. ſ e2x dx

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Q: e product (4 8 10 9)(2 7 6 11)(1 35 12)

A: