Find the slo pe of the Para bola y=X at the Point PC2,4).write an equation for the tangent to the Para bola at this Poin t.

Q: Find Equatien of the tavgnt lin tu th cuve at tk giver pointe y= sec X ,

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Q: If the curve I=3+ at? y= at + bt has a tangent line y=r-4 at t 1, what is a+b? %3D

A: We have to find a+b

Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y?, (6,…

A:

Q: Find an equation of the tangent plane and a normal line to the surface z = In Vx2 + y2 at the point…

A: Given that: z=lnx2+y2

Q: Find the arc length of the curve from z = 3 to = 6. Leave your answer as a simplified radical. f(x)…

A: Explanation of the answer is as follows

Q: (b) Calculate the arc length of the curve y from x = 1 and x = 2. +

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Q: * Find the equation of the tangent plane to the surface 9a2²-12xy = 5x2+5 at the ivon Ni Smob point…

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Q: Find an equation of the tangent to the curve given by = evi y = t – In(?) at the point corresponding…

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Q: Find the equation of the tangent plane at the point (1, 2, 7) to the surface given by x³ sin(z) +…

A: Consider a surface F(x,y,z)=0. Then the equation of the tangent plane to the surface F at the point…

Q: Find the arc length of the curve y = from x=2 to x=3 2x2 16

A: Use arc length formula

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (6,…

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2+ y², (12,…

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Q: Calculate the arc length of the curve f(x)=(2/3)(x²+1)ª2) in the interval [–1,1]

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Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

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Q: Find the arc length of the curve on the indicated interval of the parameter. x = 8t + 5, y = 5t – 3,…

A: Arc length of the curve between intervals a and b is given by:

Q: Find an equation for the tangent plane to z = cos(x2 + y2) at the point /等,0).

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Q: Find the tangent line to the cycloid (x(t), y(t))= (t – sint, 1– cost) at t = to.

A: Given xt=t-sint, y(t)=1-cost we have to find the tangent line cycloid at t=t0

Q: Show that the tangent at P(x,,y,) on the curve -1 Vx+Jy=Ja is yy, ,=a

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Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find

A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…

Q: gment JK and segment HK are tangents to rcle G. J

A: Given that:

Q: Show that the tangent at P(x,y,) the curve Vx+ Vy = Va is yy,² +xx, ² = a²

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Q: Find the speed of the cycloid c(t) = (2t – 2 sin t, 2 – 2 cos t) at points where the tangent line is…

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Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Find the arc length (8) of the curve 7 (t) = ( – 2e*, – 4e*, – 2e*) fo %3D c - - -

A: Explanation and solutions is given below....

Q: Find the point on the cycloid c(t) = (t − sin t, 1 − cos t) where the tangent line has slope 1/2.

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Q: Find the arc length of the curve y = 2/3x 3/2 from (1, 2/3) to (2, 4/ 3).

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The arc length of the the curve x =V9 - y2 - 3<y<3 is equal to Select one: О Зл O 9T О бл 18T

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In√√x² + y2, (3,…

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Q: on of the tangent to y = 3e" + 3ex that is parallel to

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Q: Show that the length of the perpendicular from the foot of the ordi- nate of any point on the…

A: We know the equation to the tangent at the point (x0, y0) is y-y0 = m(x-x0), where m is the slope.…

Q: Find an equation of the tangent(s) to the curve with paramnetric equations ¤ = 1+ VE, y = e" at the…

A:

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y²,…

A: We have to find the equation of tangent plane

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

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Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (12,…

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Q: Find an equation of the plane tangent to the following surface at the given point. 1 sin (xyz) =

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Q: Find | xdy + ydx, where C is the arc of the curve y = eª for 0 < x < 3

A: Given Data: The given integrand is: ∫Cxdy+ydx The equation of the curve is: y=ex ......1 The limit…

Q: Find an equation of the tangent plane to the surface at the give h(x, y) = In √x² + y², (12, 16, In…

A: we have to find tangent plane

Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

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Q: i Find the eguation iof the tangent line to Uthe curve y sin 2x =X COS24 at Hohe point (T7/2,…

A: Explanation of the answer is as follows

Q: Find the arc length of y = 7r +1 over the interval [0, 2]

A: y = 7r + 1 arc length=∫02 1+(dy/dr)2dr dy/dr = 7' arc length=∫02 1+(7)2dr arc length=∫02 50dr arc…

Q: Find the angle of inclination of the tangent plane to the surface 3x2 + 2y2 − z = 15, at the given…

A: We have given surface 3x2+2y2-z=15 at point (2, 2, 5)   We have to find the angle of inclination…

Q: Calculate the arc :length of the curve y = In(2x + 1) over the interval

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Q: A curve in space is given by C = { (r, y, z) = cos(nt) ', In(10 – t²), ² + 4 for t € (0, v10) Give…

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Q: Find the arc length of the curve 3y=4x from (3,4) to (9,12).

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.