Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. 3 (2t cos t)i + (- 2t sin t)j + 4/2 3/2k 0stsn r(t) = The curve's unit tangent vector is ( i+ ()j+ ( ) k. (Type exact answers, using radicals as needed.)

Q: Analyze the following equation and graph it. r(9 + 3 sin 0) = 18

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Q: Find the Cartesian equation of r2 sin(20) = 1.

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Q: Find the equation of the tangent to the function y = cos(2x) at the point where x = л/4.

A: equation of a tangent line

Q: 4. The voltage signal from a standard wall socket can be described by the equation V(t) = 225…

A:

Q: Given y= 0.3 Sin (0.2 - 0.1 x) determine • four roots • three maxima and minima • range , period…

A: To solve this, let's first understand the given function y = 0.3sin(0.2 − 0.1x): Roots:  Roots of…

Q: Use the definitions of hyperbolic functions to find the numerical value of each expression. You must…

A: Step 1: Identify the definitions for all hyperbolic functionssinh(x) = (ex - e-x)/2cosh(x) = (ex +…

Q: (g) | sin? r cos" r dr. (h) / sin" z dr.

A: (g) Given- ∫sin2xcos3x dx To find- The value of the above integral. Formula Used- cos2x=1-sin2x

Q: W Show that the curve x = 7 cos(t), y = 2 sin(t) cos(t) has two tangents at (0, 0) and find their…

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Q: 1) π.χ. (a) Find an equation of the tangent line to the curve y = tan at the point (1, 1). 4 (b)…

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Q: Using Euler's formula, el® = cos 0 +jsin 0, derive the following relationships between the…

A: We know that j=-1 or  j2=-1. The relation between the hyperbolic trigonometric function and the…

Q: Given the following sinusoidal function, what is the equation? 1 0.5 ← 1 π 2 πT x a. y=-0.5cos(3x)…

A: Here we will solve this by Option Approach. From graph we can see that y(0)= 0.5 So check every…

Q: Match each trigonometric function with its derivative. Enter the correct letter in the box beside…

A: Given, (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.