Find the unit tangent vector to the curve defined by F(t) = ( 5t, V36 – t2) at t = 1. T(1)

Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…

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Q: Determine the equation of the tangent line and the quadratic approximation to the function z = e2"…

A: Given function is: z=e2x To find the equation of the tangent at a point x=x0 to curve y=fx,…

Q: f (4, у) — 2гу + а? + 5 2.xy + x*

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Q: 3) Find an equation of the tangent line to the graph of y = (z + 4)² at z = 4.

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Q: d two coordinate points at which the tangent line to the curve given by x² – 2x + 4y² = 15 is…

A: if the tangent is vertical then dydx will be ∞x2-2x+4y2=15differentiate 2x-2+8ydydx=04ydydx=1-xsince…

Q: Find the equation of the tangent line to the curve y = x + tan x, at the point (T, T).

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Q: Find unit tangent of curve r(t)=

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Q: Consider the equation: y²³ - 3xy + x 5 = 1 a) Calculate dy using implicit differentiation. dx b)…

A: y2 -3xy+ x5 = 1Finding dy/dx using implicit differentiation 2y dy/dx - 3x dy/dx - 3y + 5 x4 = 0dy/dx…

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.