The curves 1(t) =(- 4t, tº, 4t“) and 2(t) = (sin(-t), sin(3t), t – T) intersect at the | origin. Find the angle of intersection, in radians on the domain 0

Q: Find the point on the curver(t) = (12 sin t)i - (12 cos t)j + 5t k at a distance 13p units along the…

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Q: The slope of the tangent line to the curve x = t cost and y = t sin t at the point corresponding to…

A: The slope of tangent line

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Q: Does the graph of the function y = 6x + 12 sin x have any horizontal tangents in the interval…

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Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0S0< x.…

A: Given :           r=6 cosθ

Q: Find the length of the curve 7(t) = (4 cos(3t), 4 sin(3t), 4t) for – 4 <t < 2 Give your answer to…

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Q: ind the equation for the tangent lin to y- fcx) at the specified point. fcx) where x=1 x2

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Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+ 2…

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Q: Find the length of the curve 7 (t) = (3 cos(t), 3 sin(t), 5t) for – 4 <t <1 Give your answer to two…

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Q: For the smooth curve, find any points where the tangent line is either horizontal or vertical. x(t)…

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Q: Find an equation for the line tangent to the curve at the point defined by the given value of t 15)…

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Q: 2. Find the point on the curve r(t) = (12 sin t, -12 cos t, 5t) at a distance 137 units along the…

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Q: d all points on the graph of the function f(I) = 2 sin z + sin z, 0 <I< 27 at which the tangent line…

A: Given query is to find the points where tangent is horizontal.

Q: What is the point of intersection of the tangent lines to the curve r(t) = sin(πt)i + 8sin(πt)j +…

A: Let us consider the given curve r(t) the tangent line is obtained as Find the derivative of the…

Q: find the total length of the arc of the function 6xy = x^4 + 3, x=1 to 2.

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Q: Find the length of the following curve: y = ln(cos(x)) from x=0 to x=pi/4

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Q: The exact value of the slope of the tangent line to the graph of the curve r = 9 + 8 cos(e), at e =…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j + 12t k at a distance 26p units along the…

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Q: A curve is defined by y=(1/3)sin(2x+1). Evaluate the angle between the tangent to the curve at x=2,…

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Q: Find the arc length of the curve below on the given interval. とマ 1 X=- , for 2sys4 8y 4 The length…

A: We know that length of curve x=f(y) from y=a to y=b is L=∫ab1+dxdy2dy

Q: The slope of the tangent to the curve r = 3 sin 40 at 0 = 0 is %3D Şelect one: O a. -1 3D1 O b. 0 C.…

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Q: Since the tangent equation of f(x) = x^3 – x^2 + 3x – 5 drawn from the x = 1 apse point on it is y =…

A: Given : Function  f(x) = x3 – x2 + 3x – 5 Tangent equation on the given function f(x) at point x =…

Q: Q: Find the equati on of the tangent and normal to the following curves. at the points indi cated…

A: Firstly, find the value of the x and y coordinates, that corresponds to the given…

Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: 元 ind the length of the curve x = |/12 sec't-1dt, on-낌ys이 - - The length of the curve x= V12 sec*t-1…

A: the  formula used to find the length of the curve  ds=1+dxdy2                      (1)L=∫ds…

Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

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Q: Find the equation of the tangent line to the graph of the function f (r) = -4 z+3 at the point (0,-)…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: Find the arc length of the graph of the function over the indicated interval.

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Q: Find the arc length of the graph of the function f(x) = (4/5)x5/4 over the interval [0, 4].

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Q: Find the arc length of the graph of the function over the indicated interval. =극v2 + 2)32, 0sys7 X =

A: Use length of curve formula about Y axis

Q: Find the arc length of the graph of the function f(x) = ln(cos(x)) ㅠ π [153, 5 Use the tables to…

A: Arc length of y=f(x) on a, b is  L=∫ab1+f'x2dx We have f(x)=lncosx given interval π9,π5

Q: Consider the curve where a =0 (a) Compute(t) at t = [0, +∞). (b) Find the tangent line at the point…

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Q: V. The tangent line at the point (t, y) = (- to 4'2 1 Then, the curve y = cos t is y = bt - - - a a…

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Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = 4

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: take derivative take

Q: Find the points on the given curve where the tangent line is horizontal or vertical, where:…

A: Consider  the given information: Let  r=1-sin(θ)  ,0⩽θ⩽2π To find the points where the tangent line…

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: 1.   2. slope of tangent is dy/dx.

Q: Q: Find the equati on of the tangent and nomal to the following curves at the points indi cated…

A: →Slpoe, dydx = dydtdxdt→Equation of straight line passing through x1 ,y1 with slope 'm' is given by,…

Q: Find the arc length of the graph of the function over the indicated interval. X3= 3. 2)3/2, o syS 2

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Q: Determines the length of the curve in the indicated interval x = 3 sin t+ 3t, y = 3cos t, 0stsm O 12…

A: Given curve is x=3sint+3t and y=3cost, 0≤t≤π. We have to determine the length of the curve on the…

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Q: Find the length of the curve defined by the following function for 0 <t < 2n. 7(t) = (– cos 2t)i +…

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Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

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Q: that cos (x-T) 2/a Find the puints on the curve y= 2x-3x-12.X + 20, where the tangent is parallel to…

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Q: Find F. dř for F = 5yi – (sin y)j on the curve counterclockwise around the unit circle C starting at…

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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.