38. Let r(t) = (1³ -1- 2)i + 4r* j. %3D (b) Find parametric equations for the tangent line to the curve at the point (-2, 4).

Q: Find parametric equations for the tangent line of the curve r(t) = (3+ 3/7, to – 5t2 + 4, 3t³ + 2t²…

A: Find the parametric equations fot the tangent line

Q: Identify the length of the arc having parametric equations x = t3 and y = 2t2 from t = -2 to t = 0

A:

Q: 7. Find the length along the parametric curve defined by v(t) = (t, In(cos(t))) from t = 0 andt=.…

A:

Q: Find ď²y dx² x = 3 sin t in the parametric equation y = 3 cost 0≤t≤ 2π.

A:

Q: Find the equation of the line tangent to the parametric curve (pictured below) defined by I=, y=t+t…

A:

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: 3. Let f(x, y) = xy+ y². Find the equation of the tangent line in parametric form in the x-direction…

A: Solve the following

Q: Find the equation of the tangent line to the parametric curve at (1, 3). z =1+ Int y = t +2

A:

Q: 4. Find the equation of the tangent plane to the surface Z = = 5tan(x) – sin(3y) at the point (xoyo)…

A:

Q: Find the equation for the line tangent to the parametric curve: x = t^3 - 9t y = 9t^2 - t^4   at…

A: Find slope and then use equation of tangent line

Q: A curve is defined as the parametric equations: 1 x = acose, y=-asin 0, 0<0< 2n dy where a is a…

A: on solving this we get

Q: set up intergral for the length an of the Curve 3T y%3DZ0* sin cx), 04XE

A:

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: Find the length of the curve defined by the parametric equations 3 -t, y = 3 In((t/4)? – 1) x = 4…

A: Given:- x =(3t/4)  y = 3ln((t/4)2-1)  To find:- Length of curve from t =5 to t=6

Q: Find the slope of the tangent line to the parametric curves x=3t+2, y= 2t^2+ 3t-3 at t=11 and then…

A: The given question as belonging to the derivative in which we have to find the derivative or the…

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: Find the equation of the tangent line to the parametric curve at (1,3). 2=1+ Int y =t² +2

A:

Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Find for the parametric curve x= 2e', y= sin(1+ e') dx

A:

Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

A:

Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

A:

Q: Show that the tangent line at a point P = (x0, y0) on the hyperbola(x/a)2−(y/b)2= 1 has equation Ax…

A: Given equation of hyperbola  x2a2-y2b2=1 and given point is P=xo,yo. Since hyperbola is passing…

Q: 1. Consider a fence whose base is the path with parametric equations |x(t) = cos³ t, |y(t) = sin³t,…

A: Given, A fence whose base is the path with parametric equations xt=cos3tyt=sin3t for 0≤t≤π2. Let the…

Q: Find the slope of the tangent line to the parametric curve 2te x(t) y(t) at the point P(0, 1). 2t +e…

A: xt=2t etyt=2t+etAt  P 0,1,  x=0,   y=1  ∴x=0⇒2t et=0             ⇒t=0   dxdt=ddt2t et= 2 t…

Q: 9. Find the exact length of the parametric curve for the given interval. x = 4t 2 - 3, y = 3t, 0 St5…

A:

Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t =…

A:

Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…

A:

Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

Q: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

A:

Q: 1. Evaluate the length of the curve defined by the parametric equations x = cost, y=sint, z…

A:

Q: (11) Find the tangent line(s) to the parametric curve given by * = t5 - 4t3 y = t2 at (0, 4)

A:

Q: (iii) dz< 22 + 2 where here y parametrises the straight line segment from 0 to 1- i.

A:

Q: Find the length of the arc of the curve having the parametric equations x = t³3 and y = from t = 0…

A:

Q: п 4. Find the slope of the tangent line to the polar curve r = 1 – sin40 at 0 = 4 : a. 3 b. 4 c. 2…

A:

Q: Find parametric equations for the tangent line to the curve given by x=ln(t+1), y=tcos2t, z=et at…

A:

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: 8. Solve for the critical points of the parametric equations x = t3 – 1,y = t² +t %3D

A: The answer is found in step-2.

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x? +² =…

A: Here finds the parametric equation for the tangent line to the curve of intersection.   where the…

Q: Determine the concavity of the parametric curve when t = 2 where x = 1+ t², y = t-t³ Compute the…

A: Given: The equations of parameteric curve are x=1+t2 and y=t-t3. To find: Concavity of the curve…

Q: x = 1+ vt, y = et X =1+1 Y. %3D

A:

Q: The parametric equations of a curve are given by 1 = In (Vi +1) and y= cosh(2t). dy when t = 1. dr…

A: According  to question given thatx=ln(t+1)y=cosh-1(2t)

Q: A curve is defined by the parametric equations z (t) = at and y (t) = bt, where a and b are…

A: Given,  We have  xt = at   and yt = bt  ;  where a and b are constants.  We have to find the length…

Q: Find parametric equations for the semicircle x2 + y2 = a2, y&gt; 0, using as parameter the slope t =…

A:

Q: Solve for the critical points of parametric equation x=t^3-1, y=t^2+t

A:

Q: If y = x2 is expressed with parametric equations such that = 6 when x = 1, what is ? dt dx %3D dt

A:

Q: 8. Find the curvature of the curve with parametric equation y = t³ –t and x = t? – 2t at t= 2.

A: Given parametric equations : y=t3-tx=t2-2t To find the curvature at t=2 The curvature is given by  :…

Q: What is the equation for the line tangent to the parametric curve I = 4 sin(2t) y = 4 sin(t) at t=…

A: Explanation: Given that: x=4sin2ty=4sintt=π6or 30° Concept used: The standard equation of line…

Q: 2. * (t) = t lnt and Y (t) = (t – 1)?

A: We need to find the first and second order derivative of the given function. This can be done as…

Q: Find the length of the parametric curve x = sin-1t,y = In V1– t² for 0 <t<-

A:

Q: x = V1 - i , y = t³ – 3t

A: We have to find derivative