Q: Suppose the curve C is given by the parametric equations x=1+ \t y=e' where t> 0. Find a equation of…
A: The equation of tangent line to the curve is given below
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A: As we know that the trigonometric identities:- cos2(θ)+sin2θ=1
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A: x(t) = sin(t)y(t) =csc(t)
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A: Given: The parametric equation of curve as To determine: The cartesian equation of curve by…
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A: Solution to the problem is below...
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Q: 8. Given the space curve r(t) = (sin²t, cos't, tant), find an equation of the tangent line in…
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Q: An equation of the kangent and hormat. X+sinx líne to khe curve Y =xê
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Q: 3. Consider the parametric curve C given by * = te', y =t + cos t. (a) Find the equation of the…
A: Given: The parametric equation of the curve C is x=tet, y=t+cost (a) To find: The equation of…
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Q: Given the parametric equation of a curve: x(θ) = sin θ − 1 and y(θ) = θ + cosθ a. Find dy/dx b. Find…
A: Given that x(θ) = sin θ − 1 and y(θ) = θ + cosθ To determine the Find dy/dx b. Find d2y/dx2 c.…
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Q: Find parametric equations for the line that is tangent to the curve r(t) = e^t i + (sin t)j + ln (1…
A: The given curve is Differentiating with respect to t, we get Now, we find r(0) and r'(0) and
Q: 7. Find the first derivative of y with respect to x of the following parametric equations. x = 1 +…
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Q: Consider the parametric equations x= cos 1, y = sin t, 0sts 2n. a. What curve do the points of these…
A: slope = dy/dx = dy/dt /dx/dt
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Q: 2 The diagram shows a sketch of the curve y = a sin(hx) + c , for 0 SIST. Find the value of a, b and…
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Q: Consider the following. x = sin(10), y = cos(0). (a) Eliminate the parameter to find a Cartesian…
A: Given problem:- x=sin(θ/2) , y=cos(θ/2) , -π≤θ≤ π Eliminate parameter and find Cartesian equation…
Q: 1. Find the equation of the tangent line to the curve x = e', y = et att = 1. 2. Find all values of…
A: tangent property
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Q: Find parametric equations of the line tangent to the graph r(t) = (t cos 7t)i - (t+ t)j+ sin(t)k at…
A: Given that rt=t+cos 7ti-t2+tj+sintk Tangents to the curve is given by Tt=ddtrt Tt=ddtt+cos…
Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…
A: Solution: The objective is to eliminate the parameter to find a Cartesian equation of the curve
Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…
A: At t=0,x(0)=6cos(0)=6y(0)=04-6sin(0)=0z(0)=2e3(0)=2 The point on the the curve at t = 0 is (6,0,2).
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A: Given: x=t-sint y=1-cost at t=pi/3
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A:
Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…
A: Given the curve r(t)=(4t2)i+(3t+1)j+(t3)k. We need to find parametric equations for the line that is…
Q: S* = 6 cos(t) |y = 5 sin(t) Find the exact slope of the tangent line to the parametric curve at the…
A: We have to find exact slope of the tangent line to the parametric curve: x=6costy=5sint at t=π6 For…
Q: Consider the following. x = sin(t), y = csc(t), 0 <t< n/2 (a) Eliminate the parameter to find a…
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Q: B) Find parametric equations for the line that is tangent to the curve r(t) = e'i + (sin t)j + In(1…
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Q: Consider the parametric curve x = sint + cos t, = cos² t 0 <t < 2n п Find an equation for the…
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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…
A: Consider, r(t)=lnt4i+t-4t+8j+t lnt4kWe first evaluate r(t) at t=t0=4r(4)=ln44i+4-44+8j+4 ln44k…
Q: (* = 8 cos(t) y = 7 sin(t) Find the exact slope of the tangent line to the parametric curve at the…
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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…
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A: The given parametric equations are x(t) = tan t y(t) = sect The given point t = π3 xπ3 = tanπ3 = 3…
Q: Consider the following. X = sin y = = COS (a) Eliminate the parameter to find a Cartesian equation…
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Q: For the parametric equations x = cos(t), y = 3 sin(t), find the equation of the tangent line to the…
A: Given that the parametric equations of a curve is x = cos (t) , y =…
Q: 4 cos(t) { Find the slope of the tangent line to the parametric curve at the point 1 sin(t) 6 Y =
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Q: 1. Find the tangent to the curve given by the parametric equations: X = 1/t; y= VE e-t
A: Appliaction of derivative problem
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