45. The graphs of x(t) and y(t) as functions of t are shown in Figure 16(A). Which of (I)-(III) is the plot of c(t) = (x(t), y(t))? Explain. x(t) УО) (A) (1) (II) (III) FIGURE 16

Q: 7. Find the slope of the tangent line to the graph at (1,1): x²y² – 9x² – 4y² = 0 %3D r-9r-4y = 0…

A: find the slope of the tangent line to the graph at 1,1; x2y2-9x2-4y2=0 differentiate the equation…

Q: 5. Show that the equation of the tangent to the curve y = Inx + kx at x = 1 always passes through…

A:

Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

A:

Q: 8. Find all points on the graph of y = (x + 3)² at which the tangent line is parallel to the line…

A: The given graph is y = (x +3)2 To find the points on the graph at which tangent is parallel to the…

Q: 2. Find the equation of the tangent line to the graph of y = 3cos 4x at x = 3

A: The equation of tangent line can be found by using the formula,y-y1=mx-x1Where, m=dydxx1

Q: Find an equation of the tangent line to the graph 16x4 + y4 = 32 at the point (1,2). %3D 1) 5 1 -+x-…

A:

Q: Find the parabola y= ax2+bx+c that passes through (2,1) and be tangent to the line y=2x + 4 at (1,6)

A:

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

A:

Q: Find the x Coordinate of the point on the graph of 4=x² where the to the Secant. Longent tine.…

A:

Q: 2. Compute F-dr where E= (x+ y,x-2z,z- y) and curve C is the line segment from (-3,5,1) C to…

A: Using line segment as the base of a rectangle, we choose the height to be the height of the surface…

Q: Find the points on the graph of y = 1– 5x + 3x² where that tangent line is parallel to the line y –…

A:

Q: What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?

A: Arc length is defined as the distance between two points on the curve. It is done in such as way…

Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

Q: 9. What is the equation of the line tangent to the graph of the function f at the point (1,1)? f (x)…

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: The equation of tangent line to the graph of 8x²+16y²=48 at (2,1) is A x- y - 3=0 x- y+3=0 c none of…

A: Slope of tangent line is y'

Q: 18- What is equation of the tangent line of ƒ(x)=x³- 2x² - 1 at the point x = 2 ? y=-2x+9 1903…

A:

Q: 16 12. Find the coordinates of the points on the curve y = 8 - 3- where the gradient of the tangent…

A:

Q: The curve y = a x 2 + b x + c passes through the point ( 1 , 2 ) . The line y = 2 x + 1 is tangent…

A: Given that the curve passes through a point.

Q: he line tangent to the graph of y=In(3x)+ 2x e at x =1 6

A: Equation of line is given as   y-y0 = dydxat x=1*(x-x0) Given,x0 = 1y = ln(3x) + e2x6y0 = ln(3x0)…

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: Determine the equation of the tangent to the graph of y = [2~/x - x][1+ /x - x ] at the point (1,…

A:

Q: Find all points on the graph of 3x 2 + 4 y 2 + 3xy = 24 where the tangent line is horizontal

A: Given:              3x2+4y2+3xy=24 We know the tangent line is horizontal when y'=0 So we want to…

Q: Find the tangent and normal line to the curve at the specified condition. 12x2 - 20y2 = 55 parallel…

A: Given that the curve is 12x2-20y2=55 and the required tangent and normal line is parallel to the…

Q: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

Q: Show that the solution of the equation YUx – xUy = 0 containing the curve x² + y² = a², u= y, does…

A: Given that y ux – x uy = 0, The Lagrange’s auxiliary equation for the given equation is given as:…

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: 6. Find the equation of the tangent line to the parabola y 2.x2 – x + 3 at x = 2. %3D -

A: Equation of given parabola is, y = 2x2 - x + 3

Q: 7. Find the slope of the line tangent to the curve at the point (2,1). x²y + xy² = 3x %3D

A: 7. The equation is given by x2y+xy2 = 3x                                                ......(1)…

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: B. Find the length of the curve y = x² from x 0 tox = 4.

A:

Q: 25. Find the equation of the line tangent to the curve x2 + y2 = 1 through the point (,).

A:

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

A:

Q: (3) Find an equation of the tangent line to the curve y = 2x² + 3 that is parallel to the line %3D…

A:

Q: The line that is normal to the curve x + 3xy - 4y² = 0 at (3,3) intersects the curve at what other…

A: Given: x2+3xy-4y2=0 at (3,3)

Q: 1 - Find the equation of the tangent line to the curve y = 3 5 x2 +6x 2 11 at its point of…

A:

Q: 4. Find the point(s) on the graph of (x – 1)²+ (y +3)² = 16 where the tangents are horizontal.

A:

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

A:

Q: Determine the co-ordinates of all the points at which the tangent to the curve y = 3x'e8x is…

A:

Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

A:

Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

A:

Q: 2. Find an equation of a curve satisfying the ff. condition and passing through the point (0, -1).

A: dxy-dy1+x3=0A first order separable ODE has the form of Ny·y'=MxLet y be the dependent variable.…

Q: At what point on the graph of y = (x^2)/2 is the tangent line parallel to the line 2x - 4y = 3? O…

A:

Q: 12)What is the slope at (1,2) for curve define by xy^2=4?

A:

Q: 7-The tangent of the curve x^2+y^2- 2XY3D0 at the point (1,1), is *

A: Given,           The curve is x2+y2-2xy=0 at the point 1,1.

Q: The curve y = ax² + bx+c passes through the point (3,6). The line y = 4x + 1 is tangent to the curve…

A:

Q: 4) Find the equation of tangent I point line to the circle below at point (1,-3). * x² + y² – 2x –…

A: Consider the given equation of the circle, x2+y2-2x-4y-20=0 The equation of the tangent line passing…

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

A: Find the equation of the line that is tangent to the curve y3 + 3y = x2 at the point (2,1).