The curve r (t) =< t + 5, 3t – 2, 4t + 1 > goes through the point (6, 1, 5). True False

Q: Find the length of the curve y = x³/2 from (1, 1) to (2, 2/2).

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Q: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: Find an equation of the tangent line to the curve 2(z² + y°)² = 25(æ² – y³) (a lemniscate) at the…

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Q: - 6y Find the tangent plane to the equation z at the point (12,24,4) z =

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Q: 2. Find the tangent lines to the curve y = x4 – 14x2 + 17x + 40 perpendicular to the line x = 7y +…

A: Given, y=x4-14x2+17x+40 Now differentiate with respect to x we get, dydx=4x3-28x+17 The tangent is…

Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn

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Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: The Normal to the curve 2x² – y² = 1 at the point (1,1)

A:

Q: Find all the points on the curve x² y² + 2xy = 3 where the slope of the tangent is -1. O (1,1) O…

A: We have find possible point where the slope of the tangent is -1

Q: x = e' and y = te %3D

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Q: Find the equation of the tangent line to the curve r(t) = [3+2cos(t).-3+2sin(t), 2] at the point…

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Q: Find the orthogonal trajectories of the family of curves r² + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Make the curve y= ax2+bx+c pass through (2,1) and be tangent to the lane y= 2x +4 at (1,6)

A: The given curve passes through (2,1) ⇒1=4a+2b+c                                    (1) And the curve…

Q: Find the exact length of the curve. y2 - 16(x + 4)3, Osxs 2, y > 0

A: The given equation of the curve is y2=16x+43, 0≤x≤2, y&gt;0. The graph of this curve in the interval…

Q: Determine a, b, c and d so that the curve y = ax^3 + bx^2 + cx + d will have a critical point at the…

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Q: Find the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

Q: b) Find the point on the curve y Vr that is closest to the point (7,0).

A: Find the point to the curve y=(x)^(1/2) that is closest to the point (7,0)

Q: (d) The curve y = x – x² from r = 0 to r = 2

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Q: Q4) Show that the point (-1, 0) lies on the curve 6x² + 3xy + 2y2 + 17y – 6 = 0. Then find the…

A: Put x=-1 and y=0 in the equation of curve that is…

Q: If lx + my = 1 touches the curve (ax)" + (by)" = 1, show that %3D )+) = 1.

A:

Q: 8.) Find the exact length of the curve y= over the interval (0.4]. 2 %3D -

A: Given,          The exact length of the curve y=x22 over the interval 0,4 .

Q: The tangent plane to the graph of the function :==3y+1=(1+y} at the point (1; 1; 3/2) contains point…

A: The given equation of the surface is z=x2y+1. Rearranging the above equation gives, w=z-x2y-1 Find…

Q: 9. Find the length of the curve defined by r(t) = (t, -1sts1.

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Q: dy Find for the curve x-2.x'y-20y 2 at point (-2,1). de

A:

Q: Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Since we have to find value of a,b,c and d

Q: d the equatiom of the tangent line to the curve xy – 7 = Vx + y² at the point (5,2).

A: For finding tangent line to the curve , find the derivative of the function and put the value of…

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: Find the tangent plane to the equation z = 6e" -20 at the point (4, 8, 6)

A:

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: Mike found the orthogonal line to the curve f (x) =- 3sin( zx) +1 at x=-1. In which step did he…

A: The objective is to state the step in which he made an error while calculating orthogonal line to…

Q: Make the curve y=ax³ +bx²+cx+d pass though (0,3) and have at (1,2) a point of inflection with a…

A: Given: T curve y=ax3+bx2+cx+d passes through the point (0, 3). The point of inflection is (1, 2)…

Q: Find the length of the curve r= e2θ, 0≤θ≤2

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Q: -Obtain the Cartesian equation of the curve by eliminating the parameter. 14) x = t - 3, y = t2 + 5…

A: To obtain the Cartesian equation of the given curve.

Q: The line that is normal to the curve x + 2xy - 3y = 0 at (4,4) intersects the curve at what other…

A:

Q: The slope of the curve 2y = ax + b at (1,-1)is -1.Find a, b.

A:

Q: Find an equation of the tangent plane to the graph z = Væ + y³ nt (8, 2, 4).

A: We know that equation of tangent plane to the graph z=f(x,y) at point (a,b,c) is…

Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

A:

Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: Consider the implicitly defined curve xy? +3x2 = 4. %3D Verify that the point (1, 1) is on the…

A: Consider the following curve: xy2+3x2=4 Substitute x=1 and y=1 in the above curve:…

Q: A set of direction numbers for the tangent line to the curve of intersection of S : x² + y² – z = 8…

A: The equation of a tangent line to a given surface involves the gradient of the function. When we…

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: 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: Find an equation of the tangent plane at the given point. z = In(x-2y), (3,1,0)

A:

Q: Find the equation of the tangent plane to z=6x2+2y2  at the point (1,5)

A: Given  z = 6x2+2y2  at the point (1,5)

Q: Find the length of the curve of 8x = y² + 2y-² from y = 1 to y = 2.

A: Length

Q: 7 Find the stationary point on the curve e + ye = 2e'. %3D

A: In the given question, the concept of the stationary point is applied. Stationary Point The critical…

Q: find the under the curve y=7-t^2 and above the t-axis

A: