f (x+h)–f(x) ,h+ 0 h fx) = -10x + 3h - 12h f(x) = 6xh + 3h - 5h O ) = 6x • 3h -5 fx) = 6x + 3h + 5

Q: If Fx) is an antiderivative of x2 +x1, then what is the value of F(1) - F(-1)? 3

A:

Q: then fxy Q4: If f (x, y,z) = x²y³ – y²z3 %3D -

A: we have to find partial derivative

Q: if z=x+iy then zz= 3- y² +1 3- y² – 1 G- ² |

A:

Q: Solve the linear system

A: 2x+3y=4x+2y=3over Z7

Q: F(x)=2x^3 and g(x)=-3x^2 +1, Find a)(fog)(1) b)(gof)(-1) c)(fof)(2) d)(gog)(-2)

A:

Q: • Find f" (3) for f (æ) = x³ – 2x4 + æ³ + 2x? – 7x + 3. showing the steps in your process. - -

A:

Q: Find the critical points of f(x) = x³ - 3x² - 24x. %3D

A:

Q: Find the critical points of f (x) = x³ – 6x².

A:

Q: Q1. By using simplex (Tabular) method, maximise f = 10x1 + 9x2 subjected to: 3x1 + 3x2 0

A: Consider the provided question, f=10x1+9x2subject to:3x1+3x2≤214x1+3x2+x4≤24x1,x2,x3,x4≥0

Q: Find (fo g)(x). f(x) = 5x - 2, g(x) = – x² + 4x -1 O-5x2 +20x - 7 %3D | -25x2 + 40x - 13 5x +20x -7…

A:

Q: (c) f(x) = x4 - 1 and g(x) = x4 – x³ – 3x² + 5x – 2 in F(R) -

A: HEre we have to find the GCD of the given polynomIal.

Q: 9. If f(x) = x2 - 2x + 5, what is f(x+h)? %3D A a2 -2x + h2 - 2h + 10 x2 + 2xh + h2- 2x 2h +5 C a2 +…

A:

Q: The function f(x) = 2x^3 - 27x^2 + 108x - 4 has two critical numbers. The smaller one is x = ? And…

A: Hereupon plotting we can see that horizontal tangent can be drawn at points x=3 and x=6.  Note: The…

Q: If f(x) = x2/3x +1,then f'(x) -3x2- 2х (A) V3x+1

A:

Q: Find critical points of f(x) = 3x^2 +12x -2

A: We have to find critical points of  f(x) = 3x2 + 12x - 2  To find critical points , differentiate…

Q: x – 5y = -4x - 2y %3D II at x -3.

A: Simplification of the equation helps to find the required function value. Substitution of the point…

Q: If f(x) = x²/3x+1,then f'(x) %3D -3х2 - 2х A V3x +1 9x2 +2x B V3x +1 -9x2 + 4x 2/3x+1 15x2 + 4x D…

A: Given that, The function is following, f(x) = x23x+1 We have to find the first derivative of this…

Q: Find fxy when f(x, y) = 8xeXy.

A: To find fxy when fx, y=8xexy.

Q: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: 2 Find dyif y.+3x-7 and x =, 2t +1

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: he population density of a city is given by P(x,y)= -20x²-20y +440x + 280y+200, where x and y are…

A: solution is given below

Q: Find all critical numbers of f (x) =8r³+39x²+ 18r– 4 (A -3, -

A: We have f(x) = 8x3+39x2+18x-4To identify the critical values, we differentiate and find values of x…

Q: Maximize f=-x-3y subject to -2x+y = 2 X,y >= 0

A:

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

A:

Q: Apply the Gauss-Seidel method to the system

A: the Gauss-Seidel method to the system x1 - x2 = 1 and 2x1 + x2 = 5 with initial approximation [0  0]…

Q: Maximize f = 5¤1 + 7x2 + 11a3 subject to 10r1 + 8x2 + 11a3 0

A: Consider the provided LPP problem, maximize  f=5x1+7x2+11x3Subjected…

Q: find the linearization of f(x)=x^2+4x-4 at x=2

A: Linearization formula, L(x)= f(a)+f'(a)(x-a)

Q: Find the particular solution for ysqrt(1-x^2) * y'-xsqrt(1-y^2)=0  when y(0)=1

A:

Q: Suppose g(x) = x² +2, then g(x+h) will yield to A x+2xh+h2+2 B x²+2xh +h+2 x2 +2xh +h2 +2 x²+2x+h?…

A:

Q: What is the counterexample of x/x=1

A: Follow the steps.

Q: Suppose that f(æ, y) = e-2x² – 3y² + y Then the maximum is

A:

Q: f(x, y) = 6 – V4 - x2 - y2 is

A:

Q: the extreme points of f(x,y) = 3x²y+y3-3x² - 3y² + 2.

A:

Q: What is the fxx, fyy, and fxy of f=(2x^4)+(y^2)-(x^2)-(2y)?

A:

Q: Using the principles 2y. -3y + y = 5-3" Vn20 where y=1 and y₁=1

A:

Q: -V4-x² c3-x²-y² xdzdydx, 0. 0, J-5+x²+y²

A: We will find out the required value.

Q: How do I find the possible inflection points of f(x)=a/((x^2)+(b^2))? It also states a and b are…

A: To find point of inflection we need to find x from f"(x)=0

Q: If f(x) = 3x - f(3) – g(2). 4 and g(x) -x², find the value of %3D 系 跳,, are

A: We can find the answer as below.

Q: The antiderivative of the function f(x) 6 + 8x is -8 + 3.0x2 + 6 + 4.0x2 + c 6 + 16.0x? + c -6 4.0x?…

A:

Q: The y, of y'"-y=2x²-x -3 by using variation of parameters is: .A y,(x)=Ae*+ Be- .B Yp(x) = x – 1 .C…

A: Given that  y"-y=2x^2-x-3 To find the particular solution by using the variation of parameters

Q: b) f(x, y)=-2x². + 8x − 3y² + 24y + 7

A:

Q: The discriminant of ax2 + bx + c = 0 is defined by_________.

A: The given equation is ax2+bx+c=0.

Q: f (x, y) = x² + 3y² + 4,

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

Q: Find Vf if f = 2 2 2 x² + y² + z² V.

A: Given,            f=1x2+y2+z2To find : ∇f

Q: Find / fx) + 3g(x)ldx if |F()dx = 5 and / g(x)dx = -9- -2 f(x) + 3g(x)]dx = i -2

A: We can find the answer as below.

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

A:

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

A:

Q: ,2,,2 Suppose that f(x, y) = 10x²y² + 6x? + 2y? then find the discriminant of f.

A: We have to find the discriminant from the given function

Q: Find the points of discontinuity for 3(x+2)2 a) h(x) x3 + 4x2 + x- 6 6x- x2 b) f(x) = 9 - x2

A: