23. Evaluate x² c ¥4/3 ds, where C is the curve x = t², y = t°, for 1st< 2.

Q: The line y = 3x + k is tangent to the curve y = x when k is equal to

A: Given,        The line y=3x+k is tangent to the curve y=x3

Q: What is the slope of the tangent line to the curve y = T I 7 O-2 02 0 - 17/12 01/1/01 O none of the…

A:

Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: 2 The length of the curve y = 312 between x = 0 and x = 1 is 3 %3D %3D

A: Answer is 4√2/3 unit.

Q: 13- Find the length of the curve a) r(t) = 4costi + 4sintj³ + 3tk³ 0< t < 3n b) r(t) = 4ti + 4tj¬ +…

A: Please refer the image,

Q: 4 Find all the points on the curve x2 + xy + y? = 3 where the tangent to the curve is a vertical…

A:

Q: Find the length of the curve y = V4t2 – 1 dt, 1<x<2 O 3 O 8 O 104 3. O 15

A:

Q: 4. y = x2--Inx x = 1 ve x = e

A: Topic- application of derivatives to find angle between curves

Q: Consider the curve defined by the equation y3+xy+2=0.  Show that there are no points on this curve…

A: Consider the given curve define by the equation:

Q: Consider the curve defined by the equation y³ + xy + 2 = 0. Show that there are no points on this…

A: Given Equation of curve   y3+xy+2=0  ---(1)

Q: Find the point on the curve y=x√x for which the tangent line to the curve is perpendicular to the…

A:

Q: Evaluate [(x +2y) ds, where C is the curve defined by y = √√4 – æ², for x = [0, 1

A: Here ds is arc length.

Q: 3. Find the slope of the tangent line to curve x=2sin2t, y = cos4t when t=-

A:

Q: 1. Find the set of points in the curve y = where the tangent lines are horizontal. r²+1

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: What is b &gt; 0 if the tangent line to y = bx at x = 0 has slope 2?

A: Our Aim is to find thr value of b given that the tangent line to y=bx-(i)at x=0 has slope 2.

Q: 4. Find the equation of the tangent line and normal line that passes through the circle (x – 2)² +…

A:

Q: Find the length of the curve x = 5-t, for 1 < t < 2. length = y = 3-t, z = 3t 5,

A:

Q: 2. Find the angle of intersection between the following pairs of curve. Express your answers in…

A: We know that; The expression for the angle of the intersection between the two curves is:…

Q: 10. If the curves f(x, y) = 0, y, z) = 0 touch, show that at the point of contact, dr dø dr dø dy dx…

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: Find the exact length of the curve over the given interval. 1 along 1 < y < 2. 8 4y2 ' ||

A: Find the length of the given curve

Q: show that the sum of the x-intercept and y intercept of any tangent line to the curve x1/2+…

A: Consider the given equation of curve, x+y=cddxx+y=ddxc12x+12ydydx=012ydydx=-12xdydx=-yx Therefore,…

Q: 2 2 18. At how many points on the curve + yš =1 in the TY-plane does the curve have a tangent line…

A:

Q: Sketch the two curves 7(t) = tî + t²j; t e [1, 5] and B(T) = e"î + e²r3; T E [0, In 5]. How are they…

A:

Q: ind the slope of the tangent line to the curve y = V4x – 3 at the point (13, 7).

A:

Q: 4. Consider the curve given by r³ + y³ = 9ry. Find the equation of the tangent line at (4,2).

A: To find the slope of the tangent we need dydx at (4,2)…

Q: a, given that the line ax+y+1 = 0 is tangent to the grapl

A: We have to find the value of a according to the given information

Q: 24)) Since the tangent of the curve y = x ^ 5 + ax - 3 at the point x = 1 is y = x -b, then b =?

A: Given that y=x-b is the tangent of the curve y=x5+ax-3 at the point x=1.

Q: Find the length of the curve parameterized by x = 2 + 3t² and y = 3 + 2t³ from t = 0 to t = 3.

A: To find the length of the curve parameterized by x=2+3t2 and y=3+2t3 from t=0 to t=3.

Q: 46. Show that the sum of the x- and y-intercepts of any tangent line to the curve Vx + Jy = \c is…

A:

Q: The tangent to the circle x2 +y2 +10 x+5 y= 60 at the point (2 ,4) is Select one: O None O 13 y +…

A: Given that:x2+y2+10x+5y=60

Q: 13. Find the length of the curve y4 + 8 from y = 1 to y = 4. X = 4y2

A: To find the length of given curve.

Q: 9. At what point(s) on the circle x 2 + y? = 13 is its tangent line parallel to the line 3x – 2y = 6

A:

Q: What is the aes bounded by the curve y3E betweenx-0nd 4, sbove the xis 4) 16 square units b) 48…

A: Given query is to find the area bounded by the curve.

Q: Evaluate the length of the curve: y = 3x + sinx, 0 ≤ x ≤ 1.

A: Let L be the length of curve  F(x) = 3x + sinx

Q: What is the equation of the tangent line and normal line to the curve y = at (4, - 4)? O a. TL: x +…

A: We will find the equation of tangent line and normal line as following.

Q: If y-mx+B is thế équation of the tangent line to the curve X +2xy – y+ x = 39 at x=5 with a negative…

A: At x=5 we find y The points are (5, 1) and (5, 9)

Q: (2) At what point(s) will the tangent line to y = x² – 4x + 3 be horizontal?

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (B) Find the length of the curve y 4 -Inx for 1<x <3

A:

Q: The equation of the tangent line to the curve x2 + y? = 25, at (8,-12) is. %3D 8. (x +8) + 12 12 y =…

A: differentiate equation with respect to x. 2x+2y(dy/dx)=0 (dy/dx)=-x/y so, m=(dy/dx)|(8,-12)…

Q: 19. Find the lines that are (a) tangent and (b) normal to the curve y = x' at the point (1, 1).

A: Given curve: y=x3

Q: 4.For the 2 curves xy = 8 and x2 = 64y, find the angle between the two tangent lines at the !! %3D…

A:

Q: 6 - Find the length of the curve y = (x)7 from the x = 0 to x = 4. a) O 8/27(10^(3/2)+2) b) O…

A: .

Q: 5. Find the length of the curve x = +22 from y =0 to y=3.

A:

Q: Consider the curve satisfying y" = 6x and is tangent to the line y = 5– 3x at x = 1. What is y' (2)?…

A: Given: y''=6xand tangent to the line y=5-3x at x=1To find y'(2)=?

Q: IFind the exact length of the curve x= 3t -t, y=3t² ,0<t<2 ||

A: We have to find the exact length of the curve. The length of the curve is given by

Q: py*(1 + x*)dx + 2ytan xdy ,where C is closed curve xi +yi = 1

A:

Q: Consider the two graphs y= 2x and x2 - xy + 2y = 28. The absolute value of the tangent of the angle…

A:

Q: Find the exact length of the curve. y = 4 글2-글 In(x), 1 < x < 4

A:

Q: Identify the length of the curve 1X = ²+2y — In(y + 1), for 0 ≤ y ≤ 2. - 8

A:

Q: The equation of the tangent line to the curve z? + y² = 49, at (9,-15) is , %3D 15 - (z – 9) + 15 15…

A: