Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)
A: We have to eliminate the parameter and find the cartesian equation.
Q: 32 – x² – 3y² at the 5. Find the equation of the tangent plane to the surface z = point (2, –1, 5).
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Q: Find parametric equations for line that is tangent to the curve x=cost, y=sint, z=t at the point…
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Q: 4. Find the acute angle between the curves y = sin r and y = cos r (0 < r <) at their point of…
A: We find the point of intersection by setting them equal
Q: Find an equation for the tangent plane and find the parametric equations for the normal line to the…
A: I am attaching image so that you understand each and every step.
Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…
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Q: #3. Find parametric equations for the tangent line to thể curve with parametric equations x = (sin…
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Q: Find parametric equations for the tangent line to the curve with the parametric equations x…
A: Given: The parametric equations, x = t2+3, y = ln t2+3, z = t and the point 2, ln4, 1. To find: The…
Q: The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe…
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Q: 3. Find the length of the curve y = In (cos x), 0 <x <
A: we have to find length of the curve
Q: find y'' for the curve cosx-siny=4
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Q: Find an equation for the tangent line to the curve given parametrically by x(t) 2t, y(t) 4t2 +t+ 3 =…
A: we want to find the tangent lines to theparametric equations given byx=f(t) y=g(t)The equation of…
Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…
A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…
Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…
A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…
Q: (7.5.0)- Find an equation of the tangent plane to the surface of z = sin(x – 2y) at the point %3D
A: Given F(x, y, z)=z-sin(x-2y) ∂∂xF(x, y, z)=∂∂x(z-sin(x-2y))=-cos(x-2y)∂∂yF(x, y,…
Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…
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Q: Eliminate the parameter to find the cartesian equation of the curve: x = 2 sin 0, y = cos² 0, sos…
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Q: 6. Find an equation of the tangent plane to the surface z = y² – x² at the point (-4, 5, 9).
A: Recall: Equation of the tangent plane to the surface z=f(x,y) at (x0,y0,z0) is fxx-x0 +…
Q: Find parametric equations for the tangent line at the point (cos(−4π/6),sin(−4π/6),−4π/6) on the…
A: Given parametric equation of given curve is x=cos(t), t=sin(t), z=t Differentiate with respect to t.…
Q: #5. Find an equation of the tangent plane to the surface with the equation 12x z = x²y*. y at the…
A: The given equation of the surface: z=x2y4-12xy Therefore: f(x, y)=x2y4-12xy Now:…
Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz =1…
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Q: 1. Find an equation of the tangent plane to the surface of z = sin(x - 2y) at the point (7,2,0).
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Q: 1. x (0) = 0 + cos 0 y (0) = 1+ sin 0 given that
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Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = cos t, y = tan t
A: Given that, x=cost, y=tant We have to eliminate the t and express curve in the form y=f(x). As we…
Q: 12. Find an equation for the tangent plane to the surface given by 2xy = 2z2 - ryz at the point…
A: Use tangent plane formula
Q: An equation for the tangent plane to the surface z + 3 = xy cos (2) at the point (3, 1, 0) is:
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Q: Find the equation of the tangent line to the parametric curve at the indicated point. Show all work.…
A: Equation of tangent line : y - y0 = m ( x - x0 ) m is the slope of tangent line .
Q: 9. Show that the curve with parametric equations x = sin t and y = sin(t + sin t) for 0st s 2n has…
A: Given that the curve with parametric equations are x=sint,y=sint+sint. First find the slope that is…
Q: 10. Find the value of 2 for the parametric curve xx= y = 2t2 -6 at the point (1.-6).
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Q: Find the slope of the tangent line to polar curve r=5sinθ at the point (5/2,π/6).
A: This question is related to Straight line, we will solve it using given information.
Q: Find an equation of the tangent plane to the surface y ln xz2 = 2, at the given point (e, 2, 1) and…
A: Given: ylnxz2=2 at the given point e,2,1
Q: (11) Find the tangent line(s) to the parametric curve given by * = t5 - 4t3 y = t2 at (0, 4)
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Q: Find the parametric equations of the tangent line to the curve of intersection of the surfaces x² -…
A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…
Q: Find the slope of the tangent line to polar curve V3 T r = 4 – 6 sin 0 at the point 4 – 6 Preview
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Q: Find parametric equations for the tangent line to the curve given by x=ln(t+1), y=tcos2t, z=et at…
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Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t) - sin(9r), Ostsn 9 cos (47)…
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Q: 5. Determine the slope of the tangent line, the the equation of the tangent line, and the concavity…
A: this is the equation of tangent line.
Q: 3/Find the equation for the tangent plane and normal line to the surface Z=9-x² + y² at the point…
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Q: u =1-1,y=6-2+름 x = 1-, y = 6-
A: We have given parametric equations x=1-1t, y=6-7t+2t2. First, evaluate the first derivative dydx. To…
Q: Find the exact length of the curve defined by x = 3 cos t – cos 3t and y = 3 sin t – sin 3t on the…
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Q: Determine the (1) graph, (2) initial and terminal points, (3) orientation, (4) the dy derivative and…
A: x(t)=3+sin(t), y(t)=-2+cos(t) where π≤t≤2π Graph
Q: 5. Sketch the parametric curve x = t2 – t, y = t³ – 3t and determine the location (x, y and t) where…
A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…
Q: 31. Find parametric equations for the tangent line to the curve of intersection of the cylinders x2…
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Q: 8/3 Find the slope of the tangent line to polar curve r = 8 sin 0 at the point 3.
A: Explanation of the answer is as follows
Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve
A: We have the parametric equation of curve as x=4cost⇒cost=x4 ⋯⋯1y=2sint⇒sint=y2 ⋯⋯2…
Q: eliminate the parameter to find a cartesian equation of the curve x= sinh(t), y= cosh(t)
A: x=sinht, y=cosht
Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…
A: Given:
Q: 9. Find the slope of the tangent line to polar curve r = 9 cos 0 at the point 2' 3
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- Find the Taylor series of the functionf(x) = ln(1 + 2x)−ln(1−2x) at x= 0. Find the interval of convergence for the Taylor series.Discuss the three possibilities for the radius of convergence of a Taylor series.find1) the power series using transformations of the types A-G of theknown power series of the corresponding elementary function,2) the radius of convergence,3) the interval of convergence,4) the 7-th derivative of f(x) at x = 0.
- What is the radius of convergence of the Taylor series for (x2 − 2x + 2) − 1 about x = 0? about x = 1?What are the first non-zero terms of the Taylor series, the power series written in sigma notation, and the interval of convergence for the function f(x)=ln(1+4x) with a=0?Find Taylor series at x = 0 for the functions 1/1 - 2x
- Find the Taylor series centered at zero for the function f(x) = ln(2 + x^2). Determine the radius of convergence of this series.Find the Taylor series for f centered at 4 if f^(n)(4) = (-1^n)n!/3^n(n+2) What is the radius of convergence R of the Taylor series?Find the taylor series and interval convergence. 7/3-x ln(1-5x)
- What is the radius of convergence of the Taylor series for (1 + x2) − 1 about x = 0?Determine the radius of convergence of the series 1 + x/2 + x2/3 + x3/4 +...Calculate the value of f (x) = √x = √15 ‘by expansion the Taylor series around a = 9 andconsidering the first three terms from the series. Calculate the absolute and relative errors to bemade in case of using the value found by expansion the series instead of the value of √15 =3.872 found in the calculator, as well as calculate the error percentage.