Express ax2 + bx + c as a linear combination of the functions f(x) = 5, g(x) = 4x, and h(x) = -x², thus proving that the functions span P,. ax2 + bx + c = (-x²) + (4x) +

Q: 6. Eliminate the arbitrary constants from the relation y=ax² +bx +c.

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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: Show that r: y = 3. 2n

A: Using two sectant theorem,  ∠n=12x-y  Multiply both sides by 2. ⇒2n=x-y .....(1) Using intersecting…

Q: If f(x) = | ( + 2t² + 2)dt then = (x),,f

A: f(x)=∫0xt3+2t2+2dt

Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: Express ax + bx + c as a linear combination of the functions f(x) = 3, g(x) = 4x, and h(x) = -x²,…

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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: Eliminate the arbitrary constant using any method. x^2y^3+x^3y^5 = C

A: See the details solution in below

Q: Show that $) it gly) 1-y 2

A: Recall: The domain of a function is the set of all possible inputs from the function.

Q: Use Cramer's rule to solve: X1 - X2 = a1 x1 + bx2 = a2 -2 x1-X3 = a3.

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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 & 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: Find the zero of the linear function  f(x)= x+4

A: fx=x+4

Q: Use the intermediate value theorem to show that the equation x + 2x + 1 = 0 has a solution in the…

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

A: Given function is  f(x)=6xg(x)=5x2h(x)=9x-12x2 Definition: If n functions f1,f2,f3,...fn are said to…

Q: Let f(x) = x² + 2x – 1 and g(x) = 2x – 4. Find 3f(x) – 2g(x). - -

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Q: Prove that the equation 3x² – 3x + 2 = 0 has a solution on interval [0; 1].

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Q: Let F = Z, [x] (x³ + 3x + 2) and α=x+ (x+3x+. (x³+3x+2) €F. Find a³.

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Q: Let h(x)=−2x2+x+4x2+4x−1, what is h′(−5)?

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Q: fo)-글x3-글 x2-6x +4 has

A:

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

A: Use the given information.

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

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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 average monthly bill for wireless telephone subscribers from 1985 to 2008 can be modeled by…

A: Average monthly BillBx=-1.442x+99.674 →1Given Bx=$ 43.53

Q: f(x) = {2 – 4x, if x 2 -

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Q: If f(x)=/2x and g(x)=1-x², then (gof)'(x)= %3D

A: =>(g.f)(x)=g(f(x))

Q: Given that y= (2e - 6x +5) , show that y-

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Q: Find the maximum value of ƒ(x, y) = 49 - x2 - y2 on the line x + 3y = 10.

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Q: 3- Show that the function y = x3 + 3x + 3 satisfy the y" + xy" 2y 0

A: Function does not satisfy the given inequality. See the attachment

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?…

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Q: 3- Show that the function y = x³ + 3x + 3 satisfy the y= + xy= - 2y = 0

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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: As a result of urbanization, the temperatures in Paris have increased. In 1891 the average daily…

A: Average temperature is calculated by the total sum of temperatures divided by number of observations

Q: Find a formula for the linear function with slope −3 and x-intercept 2.

A: Refer to the question.For the linear function with slope −3 and x-intercept 2, use the slope…

Q: Eliminate the arbitrary constants in y = ex + c1e2x + c2e-3x

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Q: Suppose that x and y are two positive numbers, and suppose that x + 2y = 30. Find the maximum value…

A: Given data:   The first equation is x+2y=30. The expression for the function is f(x,y)=(x+1)(y+3).…

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

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

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Q: Without using Calculus, determine whether the two variable function f(x, y) = 5x2 − 4xy + 5y2 has a…

A: The given function is f(x,y)=5x2-4xy+5y2

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

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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)?

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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

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

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