If C is a circle of radius 3 centered at the point (-4, 2 ), then evaluate £ (2y - eh (=) ) da + (6z – sin (y' + 9))dy. value = T• (Note: the factor of T is already there!)

Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: 12 of 17 > Find the equation of the tangent plane to the graph of G(u, w) = sin (uw) at the point…

A: We have to find equation of tangent plane for the given Curve.

Q: e) ay +sina-l, (,a) Equation of tangent 2.

A:

Q: Find the points on the graph of z = xy +8y where the tangent plane is parallel to 9x + 5y + 9z = 0.…

A:

Q: 13, mz1=(x² +7) and mz2 (2x² + 19)".

A: we have to find the angle between the floor and the light beam.m∠1=12x2+7°m∠2=2x2+19°sincem∠1=m∠3now…

Q: Suppose that a curve is given by the equation y2=x2+x+1 which defines y as function(s) of x Find…

A:

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: Find the equation to the tangent line y=8 sin x at point (π/6, 4) using form mx+b m= b= Both of them…

A: Topic =Derivative

Q: How many lines are tangent to both of the circles  x2 + y2 = 4  and  x2 + (y − 3)2 = 1?   At what…

A: Given: The equations of circle are given as, Consider the parametric co-ordinates for the Eq. (A)…

Q: The curve with equation 2y3 + y? – y³ = x4 – 2x³ + x² has been likened to a bouncing wagon: 3 2 1 -3…

A: Condition for horizontal tangents: dydx=0

Q: Find y in terms of x. dy aY = x 4(x 5 - 3) 2, curve passes through (1, 5) dx 17 (A y = (x5- 3) 3 +…

A: Consider a given differential equation isdydx=x4x5-32.The curve passes through the point 1,5.Express…

Q: What is y = sin (xy)

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.