Find a unit vector tangent to the curve of 25 intersection of – x? – 2y3 = z - 3 and 4y – 3z? =- x+ 6 at the point (1,1,0)

Q: Find the derivative of: h(w) = 3w + w^4/(2w^2 + 1)   [4w^5 + 4w^3 - 6w^2 + 3]/(2w^2+1)^2 [4w^5 -…

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Q: Find a point on curve y = (x-3)2 where the tangent is parallel to the line joining (4,1) and (3,0)

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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: Find the equation of the tangent plane to x^2/16 +y^2/9 −z^2/36 = 1 at the point (4, 3, 6). Simplify…

A: Use tangent plane formula

Q: Find the equation of the tangent line to the graph of a+ y = 3 at the point (1,4). 1) y - 4 = 2(x -…

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Q: the directional d + 3y2 + 5z² at pa

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Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: Investigate the stationary values of f(x, y)=x^4+4x^2y^2-2x^2+2y^2-1

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Q: Find the derivative of the vector function r' (t) = (1/-2t r(t) = n(17t²)i + √13+tj + let k 4e^4

A: Find the derivative of the vector functionr(t)=ln17-t2i+13+tj+1e4tkr'(t)=ddtln17-t2i+13+tj+1e4tk

Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

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Q: Show that the functions y1= e^t,  y2 = e^-t, and te^-t are linearly independent.

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Q: Find the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) =…

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Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

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Q: Evaluate the value of ‘a’ if the first derivative of m(x,y,z)=4-ax^2-2y^2, with respect to the…

A: Consider: mx,y,z=4-ax2-2y2 and mx1,2,3=-2. Solve for a. Calculate mxx,y,z by applying…