2) Find the clamped cubic spline for the data (1.1).(3,4), using that f'(1) - 2.f(3) = 5

Q: Find the points where the tangent line to y =2+4 is horizontal (Critical points)

A: We need to find points where the tangent line to y=xx2+4 is horizontal. In other words, we need to…

Q: 5. Find the equation of the tangent line that passes through point (1,2) to the graph 8y3 + x²y – x…

A: Proceed as shown below...

Q: Question 1 Find the total differential of the function z = 7x³y8 Odz = 7x¹y³dx + 7x³y+dy dz =…

A:

Q: 5. Find the equations of the tangent line and normal line to the parabola y = 2x² at the point…

A: Since, you have asked multiple questions , according to our guidelines we are supposed to answer…

Q: 2 Find the line tangent to the curve r3 +y3 at the point 4 (-3/3, –1).

A:

Q: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find:  Equation of tangent and normal to the curve at point…

Q: 5. Find the equation of the tangent and normal line of 2x+1 y = at point (1,1). x+2

A: A detailed solution is given below     (As per our guidelines, we have to solve only one question)

Q: Find the slope of the tangent line to the graph at the given point. (x² + y2)² = 4x²y, (-1, 1)…

A: Given equation :x2+y2=4x2ywe have to find the slope of the tangent line at -1.1

Q: 4) Find the orthogonal trajectories of the family of curves

A:

Q: (6) Find the orthogonal trajectories of the family of curves r 4C cos 0, where C being %3D…

A: We have to solve given problem:

Q: (6) Find the orthogonal trajectories of the 3C cos 0, where C family of curves r being parameter.

A: Answer

Q: Find equations for two lines through the origin that are tang net to the curve x²-4x+y²+3=0 .

A: We have given equation of curve x2-4x+y2+3=0. We also know that the slope of the line will be the…

Q: (6)Find the orthogonal trajectories for the given families of curves 2x2 – 3y = K. Where K is a…

A: We have to find out the orthogonal families of given function Given function   2x2 -3y=K  ;    where…

Q: <, y) = )-« lustrate with a sketch. y 4 3 3 2 2 2 1 -4 -3 -2 1 1 2 4 -4 -3 -2 4 -4 -3 -2 /1 -1 -2 -3…

A: Topic:- calculus

Q: Find the line tangent to the curve x + yi = 4 at the point (3V3, –1). y = x- 4 Oy = x+4 y = O y= s…

A:

Q: If ø = 4xy, find x and y components of the velocity at (1, 4) and (4, 4). Calculate the discharge…

A:

Q: The point on the curve y=vx+2 which is closest to the point (5,2) is

A:

Q: Find the tangent lines. To the cubic y=x³-2x+3 parallel to the line 10x-y=3

A:

Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

Q: Find the equations of the tangent and the normal of y = 3x2-2x+1 at point (1,2).

A:

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: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: Determine the slope of the tangent line to the graph of x2 + 4y2 = 4 at the point (√2, −1/√2).

A:

Q: If =4xy, find x and y components of the velocity at (1,4)  and (4,4). Calculate the discharge…

A: Given that, ϕx,y=4xy    ...1. Let the points be, x1,y1=1,4 and x2,y2=4,4. Consider the velocity…

Q: 20. Does the line that is normal to the curve y = x² + 2x - 3 at the point (1, 0) intersect the…

A:

Q: Find the equations of tangent plane and normal line to the graph of 9yz – Vx² – 8z = xy² – 26 at the…

A: Find the direction derivative for the function f (x,y,z).…

Q: Find the orthogonal trajectories ofthe family of curves: y = ke*

A: As per our company guidelines we are supposed to answer only first question. Kindly repost rest of…

Q: Find the equation of the normal line to the curve f (x) = 6e2x cos x at the point (0,6). %3D

A: Now point on the function is (0,6 ) . Step 1 : find the value of the derivative at x=0 . So, f(x) =…

Q: 6. Where does the normal line to the curve y = x - x² at the point (1, 0) intersect the curve a…

A: Topic = Functions

Q: The

A: Below is sketch of  the given function.    Rotation about x axis will give a volume in 3D plane.

Q: The slope of the tangent to y = 2 – x2 at the point (1,1) is

A:

Q: 5. Find the orthogonal trajectories for a family of circles tangent to the at y-axis.

A: Here we have to find the orthogonal trajectories for a family of a circle tangent to the x-axis and…

Q: Find all points on the curve 3x + 6y² = 36 where the tangent line also passes through the point (10,…

A:

Q: Find the x-coordinate of the point/s on the curve y = 2x – 3x² – 12x + 20 where the tangent line is…

A: The slope of the tangent line to the curve at point P(x,y) is given by,…

Q: Find an equation of the tangent line to the curve y = 2x2 + 3 that is parallel to the line 8x – y+ 3…

A:

Q: Find equations of the tangent line and normal line tothe curve at the given point.   y= x2 - x4 ,…

A: Given, y=x2-x4, 1, 0

Q: Find the equation of a curve in the xy-plane that passes through (1,3) and -6x(2+y) V3 – 3x2 whose…

A: The formula for the substitution method for definite integrals is given by, where g'(x) and f(x)…

Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.!

Q: 5. Find the orthogonal trajectories for a family of circles tangent to the y - axis and centers at x…

A:

Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

A:

Q: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) y = 19k

A: The objective of the question is find the orthogonal trajectories of the family of the curves.

Q: 2. What is the slope of the line tangent to the curve 8x3-y²=4 at the point (1,-2)? CAL normal line…

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: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) x2 + 2y2…

A:

Q: 6) Find the orthogonal trajectories for the given families of curve 3x - y = c.

A: To find orthogonal trajectory first differentiate with respect to x then remove constant then put…

Q: 2. Find the curve that passes through the point (1, 3) and whose tangent line at (x, y) has slope

A: Solve for the curve

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.

Q: Find the equations of tangents & normal lines to the ff. curves using the stipulated conditions. 2.…

A: Solution Given 4x2+9y2=40, m=-29we need to find the equation of tangents &amp; nomal lines

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.