Find the tangential and normal components.  r(t)=(t+1)i+2tj+t^ 2 × k     ,   t = 1

Q: Determine f g a) f(t) = cos(t), g(t) = t b) f(t)=e¹, g(t) = e' sin(t)

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Q: 2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j +…

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Q: Determine exact solutions for the equation 2sin'x – 3sinx +1 = 0 in the interval xI [a, 3n].

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Q: Find F(t) such that F'(t) = sec³ (t) tan³ (t) and F (3) = 0.

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Q: Find f if ∇f=4xyi +(2x^2+8y)j f=____

A: Find f if ∇f=4xyi +(2x^2+8y)j f=____

Q: If r(t) = = cos(-3t)i + sin(−3t)j – 10tk compute r' (t)= i+ i+ (cos (-3t))/3 and fr(t) dt= (-sin…

A: r(t)=cos(-3t) i+sin(-3t) k-10tk

Q: Let f (t) = et sin 8t Part (a) Find L{f(t)}

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Q: find all values of unknowns which satisfy the following equations: 1. (x, y, z) - 3(-1, 2, I) = (0,…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: Let u(x,y)=4x+3x2y−y3. Part (a) Show that u is a harmonic function. Part (b) Find a harmonic…

A: The given problem is to show that the given function u(x,y) is harmonic function and also to find…

Q: Find the direction field for the equation: y' = x + sin(y) + cos (x) at the point A = (0, pi3)

A: The direction field also known as slope field is used to graphically represent the solutions of…

Q: nd r'(t), r"(t), and r'(t) · r"(t). r(t) = 4 cos(t)i + 3 sin(t)j a) r'(t) b) r"(t)

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Q: Find the second derivative of the vector-valued function r(t) = (7t + 5 sin(t))i + (4t + 5 cos(t))j…

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Q: In(t + 4) sin2t Given the vector valued function 7(t) = (e-3t, t a) Find the domain of 7(t). b) Find…

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Q: apply linearity property of laplace in the equation f(t)= t cos 2t and f(t)=t^2e^-3t

A: f(t)=t cos 2tf(t)=t2 e-3t

Q: For the vector-valued function r(t) = (cos 2t, sin -(cos 2t, sin-4) 3 (4) what is the magnitude of…

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: Let F = (t + 4) i +² sin(41) j+ t^k, G = e' i+ 4f* cos(t) j+ e$t* k and 512 -i+ 4² j+te²ª k 1 +t H =…

A: Given :  F=(t+4)i+t^ 2 sin(4t)j+t^ 4 k G=e^ t i+4t^ 4 cos(t)j+e^ 5t^ 2  H = (t ^ 5)/(1 + t) * i + 4t…

Q: Exercise 68. Show that (V, B) is non-degenerate if and only if the matrix defining the bilinear form…

A: Hint: Use the given definition of non-degenerate to obtain the proof. Now, we have to proof "if…

Q: Calculate c{fie*sin (t - v) du}

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