1) Find the length of the curve? X = y 3 + -| 1 4y from y=1 to y ==

Q: Find the length of the curve defined by Y = 3x³/2 + 3 from x :3 to x = 9.

A: Question: Find the length of the curve defined by y= 3x^3/2 + 3 From x=3 to x= 9

Q: Area of a regim enilosed is by Curves y= 12 and

A: To find the area enclosed by the given two equations

Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: Find the tangent line to the curve y = x + 2x3-2x2 -3x + 3 which is perpendicular to the line x- 3y…

A: Given :y=x4+2x3-2x2-3x+3Line : x-3y=2

Q: What are the coordinates of the points in the graph of y? – x² + 6x – 13 = 0 in which the tangent…

A: y2-x2+6x-13=0 --------------(1) Differentiating with respect to x ddxy2-x2+6x-13=ddx(0)…

Q: 3. Find the tangent lines and normal lines to the curve y = x4 - 4x3 + 6x2 – 4x + 3 with slope…

A:

Q: Find the distance from the point P(2,1) to the line y = x + 2 *

A: Given point is P(2,1) and the line is given as y=x+2 1x-1y+2=0 The formula to find the distance…

Q: (6) Let a be a positive real number. Consider the curve defined by r? + y² – ry = a². Find all…

A: Given curve is x2+y2−xy=a2. Differentiate x2+y2−xy=a2 with respect to x, we get…

Q: Find the distance from the point (2, 2, 3) to the line x = 0, y = 2+2t, z = 3+ t.

A: Find the distance from the point (2, 2, 3) to the line x= 0, y=2+2t, z=3+t.

Q: Determine slope of a curve y = x³3 + 1 at x = 1

A:

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have vertical tangent line.

A: This question is taken from the tangent and line in which we have to all points on the graph that…

Q: Find the y-intercept of the tangent line to the curve y =x at the point (2,8).

A: We have given, The curve y = x3 and the point (2, 8).

Q: The slope of the line normal to the curve ex- x³ + y2 =10 at the point (0, 3) is: A. -1/6 B. 1/6 C.…

A: Equation of curve,Point

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: Q7// Find the distance between line L1:y=2 x+6 and circle with .center (1,2) and radius 2

A: The distance between the circle and the line is equal to the perpendicular distance between the…

Q: [a] Find the shortest distance from the point (2, -1, 4) to the straight line x = 2, y = 3+tand z =…

A:

Q: State the interval for which the curve y= 3x* –16x +30x? +2021 is concave down.

A:

Q: Q5) find the slope of tangent to the curve at the given points: y? + x? = y* - 2x at (-2, 1) and…

A:

Q: 3 2 1 Y from y = 1 to y = 11 - 3. ||

A: To find the arc length of the curve x=y323-y12 from y=1 to y=11. Result: Length of a curve y=f(x)…

Q: Find the distance from the point (4, 9) to the line y = 2x.

A:

Q: Find the slope of the tangent line to the curve y =x +2 x at the point (1,3).

A:

Q: Determine the length of the curve x = (y-1), where 4 <y <9.

A: Now differentiating given curve with respect to y, we get