por la función vectorial r(t) = cost i+ sen tj+t k, #/4 stSn/2. 10p

Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x2 −0.01y2 where…

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Q: Two unit vectors that are parallel to the tangent line to the curve y= 2sinx at the point (t/6, 1)…

A: To solve the given question , we must know the slope of the tangent line to the curve y=2sinx at…

Q: 6. Find the unit vectors that are parallel to the tangent line to the curve 2x3 at the point (2,…

A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

Q: Find an equation of the line tangent to the intersection of the cylinders x² + z² = 4, y² + z² = 4…

A: The parametric form of the tangent line is  x=x0+aty=y0+btz=z0+ct where, (a,b,c) is the direction…

Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: along the following paths C:(a) x=2t^2, y=t, z=t^3 from t=0 to t=1; (b) the straight lines that A ·…

A: We will use parameterization to find line integral

Q: Q2) Find the vectors the curve r(t) = at the point (11) of

A: First of all find r'(t) and the length of r'(t). Here, r'(t)=<2t,2t2,1> |r'(t)|=4t2+4t4+1…

Q: Suppose given a function f(x, y, 2) of three variables, and a point (o, y0, 20) €R. Explain in your…

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Q: Determine the interval (s) on which the vector-valued function r(t)=ti+(sqrtt+1j)+(t^2+1)k…

A: The answer is given below:

Q: For the function f(x,y)=x^3−2x^2y−y^2−y, which vector is normal to the level curve at the point…

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Q: Find the unit vectors that are parallel to the tangent line to the parabola y = x^2 at point (2,…

A: y=x2 at point (2,4) We need to find the unit vectors that are parallel to the tangent line to the…

Q: The following r(t) = (3 sint, 4 cost) represents vector-valued function. i) ii) iii) By eliminating…

A: The followingr(t)=(3sint,4 lcost) represents vector-valued function.i) By eliminating parameter 1,…

Q: Determine where the vector function r(t) = i + (14t) j is continuous. Use symbolic notation and…

A: Please see the below picture for detailed solution.

Q: 2. If a particle's position is given by r(t) = <t ₁2 cost, sint), find the IN velocity,…

A: Given: particle position, r→t=t, 2 cos t, sin t We have to find the velocity, acceleration and speed…

Q: 2² Find wheref=x² + In(x²). dx² (*) Ⓒ*) O (*+)

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: Find dy/dx: y = In [(1 + t^2)/(1 - t^2)]

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Q: Find r'(t), r(t,), and r'(t,) for the given value of to- r(t) = (5 + t)i + t°j, to = 1 r'(t) = r(t,)…

A: To find r'(t) and to sketch the curve represented by a vector-valued function and sketch the…

Q: Find the domain of the vector functions, ?(?)�(�), listed below. using interval notation. ) ?(?)=⟨…

A: To find the domain of the vector function r(t)=⟨t−3,t2−4​1​,t1/3⟩, we need to consider the values of…

Q: 3. g(x, y) = cos-1 xy, (1,0), v = î + 5ĵ

A:

Q: Find the unit vectors that are parallel to the tangent of the polynomial y= x^3 +2x + 1 at the point…

A: Consider the given function and differentiate to get the slope of the tangent.

Q: In each part we have the equation of the lines of an electric field. Obtain for each case the…

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Q: 3xyz = 63 and 3x² + 4y² + 8z² = 423 at point (−3, 1, −7). ř(t) = with -∞ < t <∞

A: The parametric form of a line that passes through x0, y0, z0 and has the direction ratios: a, b, c…

Q: Ex (50) / Find the distance from the line = 2 +t, y = 1 +t, z = -1- 2t to the plane x + 2y + 6z = 10

A: Using. Distance formula form line to plane,