Find the extrema of f(x,y) = -2x² + y taken on the graph of x + y? = 0.

Q: Solve for y at x=2: (x5 + 3y) dx - x dy = 0; x=1, y=2

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Q: Find length of curve: y=3x^(3/2) from x=0 to x=4

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

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Q: find the point (x,y) at which the graph of y=7x2+5x-6 has a horizontal tangent line.  The function…

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Q: Find all points (x, y) on the graph of ƒ(x) = 3x2 - 4x with tangent lines parallel to the line y =…

A: Since the tangent is parallel to y = 8x + 5. Hence, the slope of the tangent = slope of the line = 8

Q: Perpendicular to y + x = 0; (2, 0) on line

A: To find equation of a line ,which is perpendicular to line y+x=0,and point (2,0) lies on line.…

Q: Find the partial derivative f(x,y) = x7y fx(x,y) = ? fy(x,y) = ?

A: The given function is: f(x,y)=x7y

Q: Find general soulution (x+1)dy/dx +(x+2)y=6xe^-x

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Q: Parallel to x + 2y = 0; (1, 2) on line

A: To find the equation of line paralley to x+2y=0 and (1,2) is on the required line.

Q: What is the equation of the line normal to f(x) = 5x5 – 2x at x = -1 %3D

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Q: Find dy/dx by implicit differentiation. 8.r2y+ 5yr = -9 y 5y + 16x 2x 4x + 5y dy/dx = %3D

A: Recall: d(u.v)dx=udvdx+ dudxv d(xn)dx=n xn-1 d(c)dx=0 ; where 'c' is any constant.

Q: When we are standing at the point (1,-3), the function f(x, y) = 3x²y+xy is increasing most rapidly…

A: We have to find the direction of  rapid increase of the function using gradient of the function.

Q: Using figualve mme thod X + 2 dt 2. dy X - 29

A: To find the eigenvalues λ of the matrix A, solve the characteristic equation A-λI=0 for λ. To obtain…

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

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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: Find the maximum rate of change of f (x, y) = xy ^ 2 + root (y) at the point (2,1). in which…

A: The maximum rate of change of f(x, y) happens along the direction grad(f) at the given point (2, 1).…

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

A:

Q: How can linear approximation be used to approximate the changein y = f(x) given a change in x?

A: Given;                 y=fx How can linear approximation be used to approximate the changein y=f(x)…

Q: Solve for y at x=2: (x5 + 3y) dx - x dy=0; x=1, y=2

A: Rewrite the differential equation in standard form and solve it

Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

Q: Find an equation of the tangent to the curve f(x) = /x+ 7 that has slope %3D 4

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Q: 2.) What is the equation of the line tangent to y(x) x- 2r3+6x-3 at r =-1?

A: Follow the steps .

Q: x'dx √√x(1-x)

A:

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: Use differentiation rules to find y' = dy/dx.

A: To determine the derivative of the function.

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

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Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: Find the point (x0, yo) on the graph of y = x + 9x² + 8x – 5, at which the slope of the tangent line…

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Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: What is the derivative of y = tan-1(x2 + 1)? dy dr 2 1+( z²+1)² dy dr /1+(z²+1)² dy O dr V1+(2+1 )°…

A: To find derivative of y=tan-1x2+1

Q: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

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

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (8, -3)

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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: A heat-seeking particle is located at the point (2, 3) on a flat metal plate whose temperature at a…

A: A heat-seeking particle is located at the point 2,3 on a flat metal plate whose temperature at a…

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: 23-4z2-2一4 y = %3D 1+ Va

A:

Q: Find the equation of the line tangent to x^2 + y^2 - 6x + 2y = 0 at (0,0)

A: Implicit Differentiation In implicit differentiation, when we differentiate y, we use y' or dy/dx…

Q: Find f'(x)'f f (x)= arctan (Inx) %3D

A: Using composite function formula.

Q: Find a result by using variable separation for ý=secy b- xý = x + y

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

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Q: What is the I.F of (x^2y^3+2y)dx+(2x-2x^3y^2)dy=0?

A: Find the integrating factor

Q: Use differentiation rules to find y′=dy/dx   y = 3 · cos5 ( x − 4/x2 )

A: We apply the power rule then apply the chain rule

Q: Differentiate the function. 1 y3= (2x +3) dy dx

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Q: y 1-

A: The solution is given below in the next step:

Q: Find the derivative of the function f(z) = 3z² +7z at I = a.

A: Given,            f(x) =3x2 + 7x  and x=a

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x,…

A: SOLUTION-

Q: y' = y sec

A:

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (4, -3)

A: To solve the given line integral.

Q: Confirm the approximations by using the linear approximation at x = 0

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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.