13. Find pF dr, where P is the curve F = F(x, y, z) = (²). . cost sin t 0 ≤t≤ 27, and

Q: Find the length of the curve r(t) =〈2/5t^5/2−2/3t^3/2, t^2, 1/2t^2+t+ 7〉for 0≤t≤3.

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Q: H. Grven F(xy,2) = 9x²+y² +%Ž-37 . Frind the equation of the tangent plane and ormal line to the…

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Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

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Q: The slope of the curve y =x' + 3x² – 4x+5 at (1,5) is O a. 0 O b. 2 O c. 5 O d. 4

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Q: x = 2 + 3t, y = cosh 3t , 0 <y<1

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Q: Find the slope of the tangent line to the curves cut from the surface z= 3x? +4y? -6 by planes…

A: The solution are next step

Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: Let f (x, y) = e(3x-4y). Find the equation for the tangent plane to the graph of f at the point (1,…

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Q: Find values of a and c such that the tangent to y = ax2 + 12x + c is horizontal at the point (2,5)

A: Tangent is horizontal where derivative is zero

Q: Find the length of the curve x=t/(1+t),  y=ln(1+t) ,0≤t≤2

A: Given curve x=t/(1+t), y=ln(1+t) ,0≤t≤2. Now we have to find length of curve as shown below

Q: (47) Let C be the curve y = 5x where 1 ≤x≤9. Calculate the length of C.

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Q: V 25t* – 1 dt with 4 < x < 6. Find the length of the curve y = 1 - Length is

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Q: have found the minimum distance using the second derivative and write a thorough conclusion. to a…

A: Given:    Curve      y=lnx2   Let x,y be point on curve             Another point is 52,0 We know…

Q: 11. Use calculus to find the slope of the tangent line to the curve r? + xy - y³ = 7 at the point…

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Q: Find the lengths of the curves x = (y3/12) + (1/y), 1 ≤ y ≤ 2

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Q: tion 16 of 17 Let P be the tangent plane to the graph of g(x, y) = 18 – 9x - 18y at the point (4,…

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Q: Let f(x, y) = x³ + 2ry – y² be a func the tangent plane to f(x, y) at the poi

A: Here we have f(x,y)=x3+2xy-y2  we have to find the equation of the tangent plane to f(x,y) at point…