r(t) = ( 3t, £², √6²) for -1 ≤t≤ 4. t³ 2 Find the length of the curve r(t) : Arc length =

Q: Find the arclength of the curve x = 5t 9, y = 12t – 3 with 2 ≤ t ≤ 5. -

A: x=5t-9y=12t-3

Q: For the curve. find the slope of the tangent line at the point (0, 1). √x+y=1+x²y²,

A: Given equation of the curve  .We have to find the slope of the tangent line at point

Q: A drone flies with velocity v(t) = 3ti-fj+4k. When t = 1, the drone is at (3,2,2).

A:

Q: dy If y2=2x+3y dx find then use it to find the tangent line to the curve at the point (3,2) For the…

A: Solution is given below:

Q: Plot the curve c(t)=(2t−1,²+3). Then find the length of the curve for 1<t≤2 to two decimal places.

A: Curve is ploted and length of curve is obtained.

Q: Find the angle between the curve 2y=e-x/2 and y-axis

A: we will see in next step

Q: The length of the curve y = (2+ 2x )3/2 between x=0 and x=2 is O 41/3 O 45/2 O 43/2 O 47/3 49/6 ООО…

A:

Q: Find the length of the curve y = 4 1 between x 1 to x 2. %3D &x2

A: It is length of curve.

Q: At the point (a, b) the curve æ = t2 – 4t, y = t2 + 2t, teR has a tangent line having slope 2. What…

A:

Q: The curve = x +10g3(x²+5) has points of inflection at x = ± √10 In3 A. B. ± (In3)√ √5 Oc + 3√10 C.…

A:

Q: Find the speed of the curve F(t) = (5t² + 7, 6t – 4, t³ + 5t) at t = 4 Speed =

A: To find the speed of the curve r¯t=5t2+7, 6t-4, t3+5t at t=4.

Q: Find the exact length of the curve (x=t?cost ly=t?sint Osts2n (n? + 4)3/2 - 4] 3 a. 4 + 4)3/2 – 1]…

A: The given implicit function is,  x=t2cost, y=t2sint0≤t≤2π