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: Find the points where the tangent is parallel to y=0. y=x*-8x°+22x2-24x+9 O E 0 (1,1),(2,2),(3,0) O…

A: Given: y=x4-8x3+22x2-24x+9 And y=0, represents the x-axis. The Power law: ddxxn=nxn-1

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: Provide a set of parametric equations for the function f(x) = x² sec² (2x + 1).

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

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

A: To apply the shifting property of Laplace in the given equations.

Q: Consider (x, y, z) = 4xy²+ 3y sin(z) and at the point P = (1,2,0) calculate the directions in which…

A: Approach to solving the question:To find the directions in which the…

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: Find the directional derivative of the function pez(x, y) = cos(2x) In (5y) + sin ¹(3x) (1-²)¹/2 at…

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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: 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: 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: If, for V = V (t), tsin(V) = cos(V)+ In(t), then: a) V'(t) = 1 – tsin(V) t(t cos(V) + sin(V)) b)…

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Q: 6) y = (sin¬1 8t) (sec -1 derive

A: First, we use the product rule