4. y- /25 – x, y-0, x- 2, x-4: about the x-axis 5. x- 2y. x- 0, y = 9: about the y-axis

Q: xyz 3. If (x, y.2)= In +ef), find f,,f, and f.. 4

A: Given: fx,y,z=lnxyz4+e-3xy2z2 The objective is to find fx, fy and fz

Q: Evaluate (y – x) dx + (4x + 7y) dy. C: line segments from (0, 0) to (4, -8) and (4, -8) to (8, -8)

A: Given integral is ∫Cy-xdx+4x+7ydy Where 'C' is line segments from 0, 0 to 4, -8 and 4, -8 to 8, -8.

Q: 2. y"-y-6y = u(t – 1) – u(t – 4); y(0) = 1, y(0) = -1

A:

Q: 2x –1 1 , show that y"+ y' + xy +1 c) If y =-

A:

Q: The cubic function y = ax3 + bx² + cx + d pass through (0, -6), (1, -2) and tangent to the line 3x –…

A:

Q: 4. Šolve Člairaut equation y = xy' – 2In(y' +1)

A: The given clairuat equation y=xy'-2lny'+1 s the first order nonlinear ordinary differential…

Q: dz and dy dz 3. If x? – 3yz2 + xyz – 2 = 0, find -

A: In this question we have to find the dzdx and dzdy.

Q: 7) Suppose y varies directly with x. If y=2 when x = – - what is y when 2 X--0.3?

A: Given the data :

Q: 4. Calculate(Y/X)- – 2)* if: X = (; -) Y = (% ) z = ( ) (G Đ=z (F- )=« (4- )-

A: We will find out the required value.

Q: 31. If 9x² = y(y – 3)², show that (y + 1)² ds - dy². 4y

A: We know that Given Firstly, we find dx in terms of dy

Q: Determine a,b,c and d so that the curve y=ax^3 + bx^2 + cx + d will have a critical point at (0,-2)…

A: we have to determine a,b,c and d so that the curve y=ax3+bx2+cx+d will have a  critical point at…

Q: 5 Find the equations to both lines through the point (2,-2) that are tangent to the parabola y = x²…

A:

Q: nclosed by x = y, x = 2 - y and the x-axis?

A: And: 5/6

Q: (11 Suppose that y varies directly with x. When x = y = 30. Find y when x 7. 5, %3D

A: Two variables x and y are given. Among these variables, y varies directly with x. From this direct…

Q: 9) (3x-29 +2) ex+(39-2*-2) dyzo

A:

Q: (ost) X= 3サ-3 DiD X-2-2y ¥ーにh で3,0) D3 Dy メーと2 サ=スメート X-4 <-リ-3 toノー4)

A:

Q: -12 XY and y=-S whenxe4

A:

Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

A:

Q: Compute (T2 T)(x, y). T(x, y) (3x, 7y), T2(x, y) = (x-y, x + y)

A: We have to find T2 composition T1 .

Q: Find dy. y=5th root of x^2(8-2x)

A:

Q: 3. /4(1-)esc (1-y)dy

A: We have to solve the integral

Q: Find y' for x 3 + y-3 9. at the point (2, 1). | At (2, 1), y' Preview ||

A:

Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

A:

Q: Find fxy(x,y) if f(x,y)= e 8xy² fxy(x,y)=

A:

Q: If y = ((5z² + 8z)³ – 5-)°, then dy/dr is:

A:

Q: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

Q: 2. Differentiate the follow a) y = e 2x -ex %3D ex

A:

Q: Situation 10. In the curve 2 + 12x – x3, 32. Evaluate y' 33. Evaluate y" 34. Locate the critical…

A: We are authorized to solve only one question, with 3 subparts, please repost remaining parts…

Q: The line tangent to a curve at a point (x1, y1) is y = 2x – 2. The normal to that curve at the same…

A:

Q: What is the equation of the curve y = ax* + bx + cx² + dx + e tangent to y = 25x (2,14), to y = 2x +…

A: By verifying options and substitution of point (-1,11) it is verifying option C

Q: a) Let y" + xy' + y = 0 be given. Why does the approach y(x) := e^× does not work?

A:

Q: dy 3y y torh(x) + 2

A:

Q: hich vect וdtiolו y and 2? 1 -2 y = 1 -6 x = 2 8 -1 2 -1 5 2 -3 [ 2 -1

A:

Q: Find the equation of line passing through (5, 8) and perpendicular to y - axis. Oy = 5 Oy= 3 Ov=0 Oy…

A: The general equation of the straight line is: y=mx+c Now, the slope of the y-axis is infinity. So,…

Q: If y = x*+2 then y' at x = 1 is equal to

A:

Q: yz 4. II »z dr dy dz Jo

A:

Q: Find y' for x^2y^4−3x−3y=13 at the point (−1,2)

A: Given Data: Equation: x2y4-3x-3y=13 Point: x, y=-1, 2   Differentiate the above equation with…

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

A:

Q: 17. The line with equation y = 2x b where bis a constant, passes through the point (3, 6). What is…

A: When a line passes through a point then the coordinate  values of the point must satisfy the…

Q: Differentiate x²y3 - y2-6x=0 with respect tox. A 3x²y2-2y −6+2ху 3 2х3у2-2y - 6 6-2xy3 3ху2+у В С D…

A:

Q: 3. Find general Golution y" + y= Secx

A: Given that, find the general solution y''+y=sec3x (D2 +1)y=sec3x

Q: 3 2 | z=1 y=1 -2(x + 1)y dy dz بائية

A:

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

A:

Q: What is equation of the line normal to graph of y = x^3 + 3x^2 + 7x - 1 at the point where x = -1? O…

A: Solving the problem by finding the normal of the given equation.

Q: 4. x = 9-y2 ,-2 <y S2 about y-axis vis

A:

Q: Find fxy(x,y) if f(x,y)= e 4xy². fxy(x,y)=

A:

Q: Evaluate S. (x – y)dx + xydx where C is the y = 2x2 – 1 from the point (-1,1) to the point (2,7).

A:

Q: Evaluate B: А: Vye-y° dy 3e-4z2 dz 0, 0,

A: There is a general integral that gets calculated with the help of β function. The integral is…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.