1(t) = y = 2+ 2t z = -4 - 4t Р- (3,—6, 1) A. Find the point on l that is closest to P. Webmail B. Find the distance from l to P

Q: - 6y Find the tangent plane to the equation z at the point (12,24,4) z =

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Q: Ex: Find the distance between the pt G(4₁-4,4) and the line x=2t₁ y=Z-3, z = at +2₂

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Q: The tangent line to the graph of y = In(2x) is perpendicular to z + 4y = 1 at the point where Select…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: If the length of the curve y = 3 x7 from the point (0, 0) to the point (xo, f(xo)) is L = 8 , then…

A: Length of curve

Q: (B) The length of the curve r(t)=(1+1)i+(1-1j+r/2k from the point t=- to the point r= is 2. -IN

A: The length of the curve means the arc of the length of the curve . The arc of the length of a curve…

Q: utwards from the point (0 nd S, the top half of the

A: Given, the vector field                        E(x, y, z)=x, y, z-3this vector field can be…

Q: If C = {(x, y): 1 ≤ x ≤ 2, y = ln(x + √x² − 1)}, find the length of the curve. -

A: C=x,y: 1≤x≤2, y=lnx+x2-1

Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Find the exact length of the curve. y= In{1 – x²), o s 1. 0 sxs! 7. I Ju =

A: We will find the exact length of the curve as shown below

Q: 4. Let C be the unit circle in the xy-plane, and S be the boundary of the square with side 1,…

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Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

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Q: The Normal to the curve 2x2 – y? = 1 at the point (1,1) is: %3D 3 y =-*+ y =x+ y = 2x + 1 %3D P. y =…

A: To find The equation of normal to the curve 2x^2-y^2=1 at the point (1,1)

Q: The slope of the tangent line to the graph of z- y? = In(zy) at the point (1,1) is Select one: O a.…

A: Given the equation of the curve x2 -y2 =ln(xy) We have to find the slope at (1,1) So, the slope is…

Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

Q: (6) Find the points on the curve 5x2 + 6xy + 5y² = 9 which are nearest to and farthest from the…

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Q: r(t) = 6ti + 3/2ťj+2¢k, 0<t<1

A:

Q: If z = sin(rry). and * = t+ s, y = t2² + 8 8z when t=0, s=1. at Find

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Q: 15. When a line L is tangent to the circle 2 + v = 100 at the point (a, 6), find the equation of…

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Q: The value of the line integral S(2xy² dx + 2x?ydy + dz) along a path joining the origin and the…

A: To find the value of line integral  ∫c(2xy2dx+2x2ydy+dz)along the path joining origin and point…

Q: Find the exact length of the curve y = In(1 – x²), 0 Sx S

A:

Q: evaluate the integral over this curve

A: This question is taken from the vector calculus in which we have to find the line integral of the…

Q: Find the tangent plane to the equation z = 6e" -20 at the point (4, 8, 6)

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Q: Find the length of the curve y = V- from z =1 to r = e. 3

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Q: Find C so that the line y = 4x + 3 is tangent to the curve y x2 + C.

A: The given equations are y=4x+3 y=x2+c.

Q: Find the value of c such that line y=3/2x+6 is tangent to the curve y=cx1/2.

A: Given,  line y=3/2x+6 is tangent to the curve y=cx1/2.

Q: Find the angle between the tangents to the curve R(t) = ti + 2tj – t°k at the points t = +1

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Q: The length of the curve y = Ey3/2 between x = 0 and X 1 is %3D

A:

Q: Find the coordinates of the point(s) on the curve 2y = 10 – a² that are closest to the origin. а) О…

A: Given that

Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: Find the values of dz/ôx and az/ðy at the points 31. z - xy + yz + y -2 = 0, (1, 1, 1)

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Q: Find the equation of the tangent plane to z = e9 +x + x³ + 6 at the point (3, 0, 253).

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Q: (is)Find the eguakion af the line tangent to y=ro* át (!,10')

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Q: The tangent line to the graph of y = In(x² – 1) is perpendicular to the line a + y = -1 at the point…

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Q: (b) F. dr, C is the line segment from (1, 1) to (5, 1), F = (y, -x). 3 of 7 (c) Set up but do not…

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Q: Find the length of the curve y = a +; from a = 0 to x = 1. O None 5/2 O6/2 3 O4/2 3. 3

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Q: H.W/ A/ Find e* dr approximately using the Trapezoidal rule with n 10.

A: Given integration is ∫13ex2dx here a=1, b=3 and n=10 It means [1,3] is divided into 10 subinterval.…

Q: Let Q = 4x? + 6xy+ 4y². The points on the curve Q = 7 which are closest to the origin are:

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Q: Find the Võlumé of thé šólid generated by revolving the shaded region about the given axi About the…

A: Explanation: If we rotate the shaded region about the x-axis, we will get the cone shape. Height of…

Q: Evaluate | 9+x* dx+xy*dy along the positively oriented curve C where the C is the boundary of the…

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Q: Find the length L of the curve R(t) = 4ť²i + t° j+ 4k over the interval [3, 6]. L

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Q: The curve y = ax? + bx +c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: Explanation of the answer is as follows

Q: Find the length of the curve r(t) = t^2i − 2√2tj + (t/2 − 1)k for 0 ≤ t ≤ 1.

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Q: The expressions for and are dy A stationary point for z is

A: Note: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: If z'y +y = r dy 1, then at (0,-1) is

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find an equation for the tangent plane to z = 9x? – 8y² at the point (1, 1, 1). - = 0.

A: Here we find the equation of tangent plane.