Find the cartesian equation of the curve x = 2 sin (2t) and y = 3sin (t). Graph.

Q: Given the equation below, find 38x5 +10x⁹5y + yº 95 9 dy dx = y = = 49 dy da Now, find the equation…

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

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Q: a. Explain why the curve ²e + y²e = 4 passes through the point (0, 2). b. Give the equation of the…

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Q: Generate a 3D plot based on the equation z=sin(x) +cos(y), both x and y range from 0 to 2 pi. Please…

A: [x,y]=meshgrid(0:2*pi); z=sin(x)+cos(y); surf(x,y,z)

Q: 1. a) Find dy for the equation 4x²y ² - x ³y = 3 dx b) find the x-coordinate of each point on the…

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Q: The equation below defines y implicitly as a function of x: 2x2 + xy = 3y2 Use the equation to…

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Q: 10b. Find the parametric equations of the tangent line to the curve at t =1.

A: Given: The position vector is of a particle in space at a time t : r→(t)=<t+1,t,1t>=<x, y,…

Q: Calculate y' and y" for y = x°e². (Simplify answer.)

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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.