Express ax + bx + c as a linear combination of the functions f(x) = 3, g(x) = 4x, and h(x) = -x², thus proving that the functions span P. (-x²) + (4x) + ax2 + bx + c = 3

Q: Verify that g'(x) 1 where g(x) = v2x – 3. %3D V2r – 3

A: Giveng(x)=2x-3.To verify g'(x)=12x-3  is the derivative of g(x).

Q: If f(x)=-2x+1 and g(x)= vx² –5, 16. %3D %3D find (gof \2)

A: Given that:fx=-2x+1 and gx=x2-5To find g∘f2

Q: solve by finite difference ²x - ²)x=t dt²

A:

Q: Show directly that the given functions are linearly dependent on the real line. That​ is, find a…

A:

Q: Show that Y1 = X1/X2 and Y2 = X1 + X2 are independent and that Y2 isχ2(r1 + r2).

A: Given Y1=X1X2Y2=X1+X2

Q: Show that the equation x-4y+7z=14 , 3x+8y-2z=12 , 7x-8y+26z=5 are not consistent

A: Show that the equation x-4y+7z=14 , 3x+8y-2z=12 , 7x-8y+26z=5 are not consistent  We use Cramer's…

Q: Determine whether there exists a constant c such that the line x + cy = 1: passes through (3, 1).

A: We have to determine the value of constant c such that the line x+cy=1 is passing through the point…

Q: Express ax2 + bx + c as a linear combination of the functions f(x) = 5, g(x) = 4x, and h(x) = -x²,…

A:

Q: A chemical manufacturer wants to lease a fleet of 28 railroad tank cars with a combined carrying…

A:

Q: Determine whether the statement is true or false. fxy дх ду True O False

A: We have to determine given condition it is true or false

Q: If f(x, y) = In (2x-3y), then find of ||

A: We can solve this problem using partial derivatives.

Q: Write the dual of the LPP Max z = 4x1 - x2 + 2x3 Subject to x1 +x2 < 5 2x1 + x2 < 7 2x2 + x3 2 6 xi…

A:

Q: Find the consumer and producer surpluses (in dollars) by using the demand and supply functions,…

A: Given information:- Find the consumer and producer surpluses (in dollars) by using the demand and…

Q: If g(x) = 2x + 10 and h(x) = 3x - 2,                        3 Find: - g[h(x)] = and express in its…

A:

Q: If f (x) is a linear function, f (1) = 0, and f (2) = 1, what is f (3)?

A: fx is a linear function such that f1=0 &amp; f2=1

Q: 2X + 5YZ  is NOT a linear function. True False

A: In general the linear function can be written as fx=mx+b where m is slope and b is intercept. The…

Q: Show that if f and g are linear, then so is f + g. Is the same true of fg?

A:

Q: Let h(x) z² –3z+2 -z² –4x+4' what is h' (-5)?

A:

Q: find a formula for the linear function f(x) that satisfies f(5)=7 and f(0)=-3

A: Given information:f(5)=7 and f(0)=-3

Q: The fixed-points of f(x) = (x² + 2) are_ and

A:

Q: If f(x) = x2 – 5x + 7, what are the co – ordinates of the minimum of y = f(x – 2)?

A:

Q: Find the constant C such that .4 x3 - 3x + 5 < C,

A: x3 - 3 x + 5≤c x∈{0,3}

Q: fo)-글x3-글 x2-6x +4 has

A:

Q: Show that Live - de = In(V5- 2). -1 Vx2 + 2x +2

A: We need to show that, ∫-11-dxx2+2x+2=ln5-2

Q: Show that if f and g are linear, then so is f + g. Is the same true of f g?

A: Let f,g:V→V are linear maps To show that f+g and fog are also linear

Q: Find the linearization at x = a. g(x) = 20x² x - 3 a = 12

A:

Q: Given that x3y2=ax+y, express y′ in terms of x and y (a is a constant

A: Given x^3y^2=ax+y'

Q: The fixed-points of f(x) = (x² + 2); are and

A:

Q: The fixed-points of f(x) = (x² + 2) are and

A: Solution :  The fixed point of the function f(x) is  f(x) = x  Since, given function is  f(x) = 1/3…

Q: Investigate the based on linearization 3 x = x₁ - x₁²³²+x₂z xr 394 - 292 6 Ac

A: This is a question of equilibrium and stability.

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: 1. Use the chain-rule and find x and ÿ in terms of x, i, and ä if: а) у3 4x? b) y= 10x3

A: To find y" in terms of x, x', x".

Q: f(x) = 2x, g(x) = 3x², h(x) = 5x – 8x²

A:

Q: Derive all the possible equations of x. Given : (x-2)^2+lnx=0

A:

Q: If w = (4x-8y)(-3x+5y) , find Wxy at point (2,1) ху

A: Given that, the function w = 4x-8y-3x+5y To find the Wxy at point (2, 1)

Q: Among all pairs of numbers (x, y) such that 2x +y = 9, find the pair for which the sum of squares, x…

A: NOTE: Refresh your page if you can't see any equations. . the given constraint is

Q: The linear function f(x) = ax + b is a constant function if?

A:

Q: Show that the three functions: f₁(x) = ex-8f₂(x) = exf3(x) = 4(2x-2) are linearly dependent.

A:

Q: Find the point at which the line f(x) = - 3x +8 intersects the line g(x) = -5z + 16 %3D %3D

A: Given f(x)=-3x+8 g(x)=-5x+16

Q: For f(x)=3xv(4-x²) determir within its domain..

A:

Q: Eliminate the arbitrary constants of: x^2=Axy+By

A:

Q: Suppose z is a function of r and y, and x² + y² + z² = xe² + ye² + ze³. Solve əz əz for and əx ду

A: Topic = Derivative

Q: The fixed-points of f(x) = (x² + 2) a and

A:

Q: Eliminate the arbitrary constant c from the relation y - cx = 3c +1.

A:

Q: Express ax? + bx + c as a linear combination of the functions f(x) = 5, g(x) = 4x, and h(x) = -x²,…

A:

Q: O Express : 2 as a linear combination of

A: By using definition of linear combination

Q: Let h(x)=−2x^2+x+4/x^2+4x−1, what is h′(−5)?

A:

Q: Determine whether 2 4 are linearly independent.

A: The vectors are independent if a120+b11-1+c142=000 which implies a=0,b=0,c=0…

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:

Q: Find the equation of the line through the given pair of points in standard form using only integers…

A: