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

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