r (t) =< 2 – t, 4t + 3, 6 > is a line O circle helix O parabola

Q: - Compute 5y dr a dy, where C is the arc of the parabola y = from (-2, 4) to (0, 0).

A: The line integral of the function with respect to x, y is solved using the formula…

Q: Find an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

Q: Find the radius of curvature of the parabola y² = 4px at (0, 0).

A: Given that the parabola y² = 4px  To Find the radius of curvature of the given parabola at (0,0).…

Q: Set up an intergal of the Curve for the length 3T Y%3DZE* sin (x), O4 xE 2

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Q: Do the curves ri(t) = (t² + 3, t+1, t² – 5) and rž(s) = (4s, 2s – 2, s + 1) intersect? If so, at whi…

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Q: Find the exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

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Q: Find the exact length of the curve. = 글Vy (y-3), 16 sys 25 X =

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Q: Find the length of the curve x = 5-t, for 1 < t < 2. length = y = 3-t, z = 3t 5,

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Q: Evaluate Iz = y", 2ry ) · d7 where C3 is the arc of the curve x = 3 – 2y that extends from (7, –2)…

A: we have to evaluate the following

Q: Show that the exact length of the curve below is y = Vr - r² – sin ¬1 (V7)

A: SOLUTION-

Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Q3 Find dyldx on the graph y secx + y = cos2x at point (1, 2).

A: We have to find the derivative of above function at (1,2) Please see the explanation below

Q: Find the arclength of the curve y = (x² − 4)² on [2,4].

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Q: Find the exact length of the curve. y2 - 16(x + 4)3, Osxs 2, y > 0

A: The given equation of the curve is y2=16x+43, 0≤x≤2, y&gt;0. The graph of this curve in the interval…

Q: set up intergral for the length an of the Curve 3T y%3DZ0* sin cx), 04XE

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Q: dz where C denotes a 22 Contour C=2e' with a deleted onigin. (2#0)

A: For the solution of the problem follow the next step.

Q: Set up an intergral for the length of the curve, 04X y%3DZE* sin cx), O4 XE

A: Explanation of the answer is as follows

Q: Compute the length of the circle of radius r defined parametrically by = 3 cost, y = 3 sint ; 0 s t…

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Q: whose x-coordinates are equally ine with parabolic runout conner

A: Given as.     python code :

Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

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Q: 19. Evaluate Scx ds, where C is a. the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).…

A: Part (a)

Q: If lx + my = 1 touches the curve (ax)" + (by)" = 1, show that %3D )+) = 1.

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Q: Find the shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: dy Find for the curve x-2.x'y-20y 2 at point (-2,1). de

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Q: Find the exact length of the curve. y = 4 =Dx2-을 In(x), 1sxs6 =

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Q: Compute the length of the curve x = 2y3 + 1/(24y) from y = 1 to y = 3.

A: Given: x=2y3+124y1≤y≤3

Q: Find the curvature k of the curve given by r(t) = (2t²,t, ¿ť²)

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Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

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Q: Find the shortest distance from the point (0,2,3) to the plane x+2y+z=1

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Q: Find the curvature of the plane curve y = -t at the point t = 2. к(2) -

A: Given:y = -t4differentiating with respect to t, we get:            y' =     d(-t4)dt…

Q: What is the aes bounded by the curve y3E betweenx-0nd 4, sbove the xis 4) 16 square units b) 48…

A: Given query is to find the area bounded by the curve.

Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: What is the length of the curve I= cost +tsint, y=sint - tcost, (0 <t< 2n) ?

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Q: Find the arclength of the curve: y = 5(x + 2)3/2,2 <x<7

A: The arc length is given by, S=∫ab1+f'x2dx   Find the derivative of the function y=5x+23/2.…

Q: ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

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Q: Find the equation of the tangent plane to the surface -2² at the point y = 2x2 – (0, –1,2)

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Q: Find the lenght of the curve y = x- tnx, 1+/dy 2. dx %3D %3D

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Q: Find the curvature K of the plane curve y 3 at x = 3. 2х + K =

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Q: What is the longest distance from the curve x ^ 2 + xy + y ^ 2 = 16 to the origin?

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Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

Q: Find the tangent line to the ellipse x^2+4y^2=8 parallel to the line x+2y=6.

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Q: Compute y ds over the part of the parabola y =2Px, for P > 0 starting at (0,0) at (2P,2P).

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Q: ind the equation of the tangent line to right branch of the hyperbola == sec t, y= tant, 2 - sts at…

A: Topic:- application of derivatives

Q: Q2 Calculate 8- Z -dz, (4 – 2) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: 3 dz where C, is the top half of circle with radius (b) Compute the upper bound of 2,

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