a) Sketch the curve r (t) =< 2 cos t, 2 sin t, 3 > Name the curve.

Q: Find the coordinates of the inflection point of f(x)=cot(x) that is nearest (but not on) the origin…

A: Consider the given: fx=cotxAn inflection point is a point on the graph at which the second…

Q: Find the expression for the tangent slope dy/dx for points on the Polar curve r= 6 +12 cosθ

A:

Q: Find the for the radii vector maxima and minima the Curve 2. a 2. sin'o Costo

A: Our objective is to find the maxima and minima for the radio vector of the curve.

Q: Find the tangent plane to the equation z = 2y cos(5z – 4y) at the point (4,5, 10) z = 2y- 2= 0 X…

A:

Q: Which of the following is the tangent equation drawn to the pi/4 point on it? y = 25 - tanx curve…

A: This question is based on straight line. The general equation of a straight line is            y =…

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A:

Q: graphically represent the curve described by the following functions f (t) = (sin t, 2cos t)

A: Parametric curves: Let f and g be continuous functions on an interval I. The parametric equations…

Q: Find the slope of the tangent line to the polar curve r = 2 sin(36) at the point corresponding to =…

A: NOTE: Refresh your page if you can't see any equations. . substitute the given angel

Q: 5. Find the equation of the line (in Cartesian coordinates) tangent to r = 1– sine at the point (5).

A:

Q: Locate the center of the curve r = 4(sinθ + cosθ)

A: NOTE: Refresh your page if you can't see any equations. . the given curve is ...............(1)

Q: Find the equation of the osculating plane of the curve (a sin u + b cos 4, a cos u + b sin u, c sin…

A:

Q: Find the slope of the tangent line to polar curve r = 8 – 7 sin 0 at the point (8 %3D 2' 6

A: Given the equation of polar curver=8−7sinθ       .......(1)(8−72,π6)

Q: Consider the parametric curve C defined by  x = x ( t )  and  y = y ( t ) . (a) Explain how to…

A: The parametric curve C defined by  x = x ( t )  and  y = y ( t ) has a horizontal tangent if slope…

Q: Let t be the angle between 0 and such that sin t Then cos t sin(-t) cos(-t) tant =

A: Solution ) sin t = 1/4    t = sin-1(1/4)    t = 14.48 Cos (14.48) = 0.968 Sin(-t) = - sin t Sin (-t)…

Q: Let y= 3 cos x-5 cot x+ csc x tan x, then the slope of the tangent line at x = is 4

A:

Q: determine the slope of the tangent line to the polar curve r = 3 + 8 sin 0 at 0 =

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.