3. Find the equation of the tangent line to the curve C given by the parametric equations x= e', y= In(t+1) at the point corresponding to t=0.

Q: The x- intercept of the tangent line to the polar curve r=(1+sin 0) at 0=" is

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Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t). dz 4cos4t…

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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. x-…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: The given curve is rt=t2+1,4t12,et2-t. Notice that the given curve satisfies t=1(If t=1 is plugged…

Q: (a) Find the slope of the tangent line to the parametric curve x = t/2, y = t 2 + 1 at t= −1and at t…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 0, y = a sin 20 from 8 =…

A: We are asked to find the length of the curve whose parametric equations are as follows:…

Q: Find the second derivative of the parametric equation ; x = t3 + 1, y = 4t2 −4t.

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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: The equation of the tangent line to the parametric equations, x =t +sint, y 4t-cost att 0 is y = -1…

A: As we know that; The slope of the tangent line to the given curve is equal to the first derivative…

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint); + In…

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Q: Find the derivative 4cos4t sin4t 2cot4t -1/2 cot4t Other: of the parametrically defined curve : x(t)…

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Q: (a) Find the slope of the tangent line to the parametric curve x = 3cos t, y = 4sin t at t =…

A: Given, x=3cost,y=4sint at t=π4 and t=7π4. Differentiate the functions x and y with respect to t.…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: :2 cos(t) y = 3 sin(t) T = Find the slope of the tangent line to the parametric curve at the point 4

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Q: Consider the smooth parametric curve defined by the equations = t (t² − 3) = 3 (t² − 3)' X Y where…

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Q: A curve is defined by the parametric equations: x(1) = e' cos t, y(t) = e' sint d²y dy and dr of the…

A: It is given that, x(t)=et cost,y(t)=et sint   It is known that, dydx can be found by chain rule and…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: 2. Calculate the derivative dy for the parametric equation x = t² + ³ + ln(4t+1), y=e5t² giving your…

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Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t).

A: We have to find dy/dx.

Q: 3. Find the slope of the tangent line to the polar curve, r = 2 cos 0, at the point specified by 0 =…

A: Given:        r=2cosθ at the point specified by θ=π3.

Q: (a) Find the slope of the tangent line to the parametric curve x = t² + 1, y = t/2at t = −1and t = 1…

A: Given,                          x=t2+1,   y=t2,    and               t=-1,            t=1

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Parametric equations for a line:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: The given parametric equation is: x=5 ln t  ,   y=4t   ,      z=t3 Given point is:  (0, 4, 1) From…

Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: Suppose a curve is traced by the parametric equations x = 2( sin(t) + cos(t1) %3D y = 23 – 6 cos (t)…

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Q: 1. Eliminate the parameter to find a Cartesian equation of the curve given parametrically by (x(t),…

A: Recall: sin2t+cos2t=1

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: 1. Evaluate the dy for parametric equations x = 3t³ - 3 and dx y = 3t² - 6t using parametric…

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Q: The x- intercept of the tangent line to the polar curve r=3(1+sin 0) at 0=" 프 is

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Q: Find the 1st and 2nd derivatives of y with respect to x from parametric equations. a). x=3 (t + 2)…

A: First differentiate x and y wrt t then divide

Q: Find parametric equations for the tangent line at t=3 for the motion of a particle given by…

A: To work out the equation of the tangent in terms of t

Q: Find a parametric equation for the tangent line to the curve defined by r(t) = when t = 1.

A: Given is the equation of a 3-dimensional parametric equation, to find the equation of the tangent we…

Q: x = 2 cos(3t) – 4 sin( 3t) IT t = 2 y = 3 tan( 6t)

A: given,        x=2cos3t-4sin3t   and y =3tan6t

Q: 8. Find parametric equations for the tangent line to the curve r(t) = (t² +3t +2, e' cost, In(t +1)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the derivative of the following parametric equations. (a) x = t2 + 5t + 4, y = 4t (b) x = 0 –…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Answer

Q: 2. Find parametric equations for the tangent line to the curve r(t) = (t8,t³,t7) at (1,1,1).

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Q: Find the parametric equations for the tangent line to the curve x=t^4−1, y=t^3+1, z=t^2 at the point…

A: Consider the given curves and points.

Q: ) Find the equation of the tangent line (in terms of x and y) to the parametric curve at the given…

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Q: 2 Calculate the (d^n*y)/(dx^n) derivative of the curve with the parametric equation x=lnt, y=t^alpha

A: The given problem is to find the nth derivative of y with respect to x of the given parametric…

Q: x = 3 ln(t), y = 4t1/2, z = t3; (0, 4, 1)

A: Given Data: x=3lnt ......1y=4t1/2  ......2z=t3      ......3 x0, y0, z0=0, 4, 1   For the specified…

Q: Calculate the derivative dy for the parametric equation x=t7+t³+ln(5t + 1), y = e4t²_ +t6 giving…

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Q: Find the derivative of the following functions/parametric equations. 4. e2x cos y + y2 = 1

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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

Q: VI. x = v1 - t , y = t³ – 3t

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Q: 7) Let x = t – sin(t) , y = 1– cos(t). Determine the equation of the line tangent at t = n.

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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