Q- Find Domain and Range of the function 1) y= V2- Vx 2) y = 2eX - 3 |

Q: Find equations of both lines through the point (2, –3) that are tangent to the parabola y = x2 + x.…

A: We have to find equations of both lines through the point (2 , -3) that are tangent to the parabola…

Q: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x %3D

A: Given , the function f(x) = x2 - 2x Now we find      f(1) = 12 - 2•1 = 1 - 2 = -1,…

Q: 13. y = x'/9, 0 sxs 2; x-axis

A: The formula for area of revolution of a curve on interval [a,b] about x-axis is given as…

Q: Find the area of a triangle bounded by the y axis, the line f(z) = 9 -1, and the line perpendicular…

A:

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: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x

A: Rule:-equation of line passing thraught (x1,y1) and (x2,y2) is y-y1=y2-y1x2-x1(x-x1)

Q: If y2 is negative, then y1 + y2 will lie _______ y1 by a distance equal to ____.

A: If y2  is negative, then y1+y2  will lie _______ y1  by a distance equal to ____.

Q: Obtain the general solution using variation of parameters y''+y = (csc³x) (cotx)

A:

Q: Find the local extreme values of ƒ(x, y) = x2y on the line x + y = 3.

A:

Q: Solve for the domain and range of. f(x,y,z) = %3D V4-x2-y²

A:

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: 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: I have equation 3x(y-x)=0. Is it true that x here is equal to 0 and y is equal to x? How can I show…

A: To check:  Whether x here is equal to 0 and y is equal to x. Given information: The equation is…

Q: Solve 2sinx- V3 = 0 on interval [0,2 t)

A: We have to solve  2sinx - √3 = 0 on interval [0 , 2π)  Since ,  2sinx - √3 = 0  2sinx = √3

Q: Find domain and range F(x,y)= Vx-1

A: Since you have asked multiple questions in a single request, as per policy, only the first question…

Q: Find the interval(s) where the function y = x – 2x² – 7x + 2 is concave down. Justify your answer.

A: Find the double derivative of y and then equate it to zero.

Q: Find the indicated value of the function f(x,y,z)=2x-7y + 4z³ -7. f(6, -5,3) f(6, -5,3)=

A:

Q: Find fx, fy, fz f(x,y,z) = x – V2y² +z?

A:

Q: 13. y = 5 – Væ, x = 1, x = 4 and the x-axis.

A:

Q: Jzu t>o ニ C <x<L ulx,o)- f(x) -g(x) 4(et)-U,lしt)-。

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: Find fxy(x,y) if f(x,y) = (x² + y²)6.

A:

Q: By using false position method find f(x) = e* - 2 u %3D

A: Attached solution :

Q: Find the values of ôf / ôx at the point (4,-5) if f(x, y) = x +3xy + y-1

A:

Q: dz Find at (2, -2, 1) if x² + y? + z2 6xz + 6yz + 21

A: Given equation is x2+y2+z2=6xz+6yz+21 We have to find ∂z∂y at 2,-2,1

Q: The shortest distance from the point (5, 10) to the curve x2 = 12y is: 5.127 6.445 4.331 3.474

A:

Q: 3) Calculate the length of the curve interval [-2₁2]. y = x²/2 on the

A:

Q: If x2 + y2 = 4 which has domain Dr=[-2,2] range Rf=[0,2]. Shrink and stretch it vertically by 3…

A: We are given:  x2+y2=4⇒y=4-x2=f(x) For shrinking vertically by 3 units , we have: f(x)→13f(x) Hence,…

Q: 2 The Range (Ry) of y = v9 – x² -

A:

Q: Solve for x, y z from X - 1 1 2 Z 3. 6 6

A: 2x-113y=2z66

Q: II. Verify that ду дх дх ду 3 2 2. f(x, у) %3Dх'у? — ху 'y² – xy ³

A: Given function: Now,

Q: What is the equation of the line tangent to the function y = 2³+7x² + 5x - 2 at x = 0? There can be…

A: Application of differentiation

Q: If f(2) = 3 andf'(2)=-1, find the equation of the tangent line when x = 2 %3D %3D %3D

A:

Q: D.(1,2), where f(x, y) 14x-y in the directionof v (2,-1)

A:

Q: Find fxy(x,y) if f(x,y) = (x² + y²) 7. fxy(x,y) = ...

A:

Q: Lion 1-y If x = Show that 1+y dy V1-y

A:

Q: 11. Perpendicular to 5y = 2x – 6 and passes through the point (-1, 5)

A: Given, The line is perpendicular to 5y=2x-6 and It is passing through the point (-1, 5). Concept…

Q: What are the coordinates of the points in the graph of y? - - x2 + 6x – 13 = 0 in which the tangent…

A: Note that the slope of a horizontal line is zero. Also the slope of a tangent is given by the…

Q: Decide whether it is possible to solve the equations xu? + yzv + x²z .xyv³ + 2zu -- u?v² = 2 for (u,…

A: 3.7 Given equations are xu2+yzv+x2z=3xyv3+2zu-u2v2=2 The points are  (x, y, z)≈(1, 1, 1) and  (u,…

Q: Find the slope for f(x,y) = xeyat P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: We have to find slope

Q: Suppose that f(x, y) = 32 y at which {(x, y) | æ² + y² < 3²}.

A:

Q: Find fx(x,y) and fy(x.y). Then, find fx(- 4, – 1) and fy(- 1,3). 23| f(x.y) = In |8 + 5x²y³|

A:

Q: f (x, y) = x² + 3y² + 4,

A: Supposing the question is asking to find the local minima value.

Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7.

A:

Q: f(x) = avbx – c - the x -axis and the line x = 17 using Trapezoidal Rule with 6 equal intervals if a…

A:

Q: Use the characteristics method to solve the problem U, +3yU, = 2U , U(x,1) = f(1+ x,)

A:

Q: Find equations of both lines that are tangent to the curve y = x3 - 3x2 + 3x - 3 and are parallel to…

A: The given curve is represented by y = x3 - 3x2 + 3x - 3 and are parallel to the line 3x - y =…

Q: f(x,y) = /² + y?

A:

Q: Compute Δy/ Δx for the interval [2,4] where y = 5x−7.

A: ∆y∆x for function y=f(x) for the interval [a,b] = f(b)-f(a)b-a

Q: Find equations of both lines that are tangent to the curve y=x3 -3x2+3x-3 and are parallel to the…

A: Given, curve y=x3 -3x2+3x-3 and tangent are parallel to the line 3x-y=15.

Q: Solve for the domain and range of. f(x,y,z) = V4-x2-y?

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.