Express ax? + 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: Show that the equation f(x) =x+3x-1%=Ø %3D has at least one solution,

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Q: Let Ax) = x³ + 9x² – 6x + 2. Find f (x) and f"(x), and then solve f"(x) = 0.

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

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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: 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,…

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

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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: 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: If f(x) = - 2x + ax² +2 and f(2) = 2a, find a. %3D 2.

A: A function is a relation connecting two variables, in such a way that one  variable varies with the…

Q: Find the zero of the linear function. f(x)=3/4x-18

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Q: Suppose f is a linear function and that f (2)=7 and f (5)=7.1.  Then the slope of is postive   true…

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Q: Let f and g be linear functions with equations f(x) = m1x + b1 and  g(x ) = m2x +b2. Is f ° g also a…

A: The given linear functions are fx=m1x+b1    and  gx=m2x+b2. This implies that,…

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

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Q: 2) If g(x) =3 - 2, find g-(x). %3D H-3

A: Given,           gx=3x-3-2

Q: Suppose that f is a linear function with slope 4 and that f(4) = 4. Find the equation for f. (Use x…

A: Given : Suppose that f is a linear function with slope 4 and that f(4) = 4.

Q: If F(x)=[ -dt , find F' (3). 2t 2

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Q: Q4) Find the linearization of: f(x) = x³ + 10 when a = -3

A: l(x)=f(a)+f'(a)

Q: The function of two variables f(x.y)=(y-2) x^2-y^2 has:

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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

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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: f(x) = {2 – 4x, if x 2 -

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Q: If f(x) = x² + 3, then ƒ(x + h) =? Select one: a. x² + 2xh+h² + 3 O b. x² + 3 + h² c. O d. x² +3 + h…

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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: y = C₁e⁻³ˣ - 2c₂e⁻³ˣ

A: differential equation

Q: Which is equal to (4) (x) given that g(x) =1 – 3x and h(x) = Vx? %3D Vx – 3xVx - 3xVx X. Option 1…

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

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Q: If the profit function for a product is P(x) = 5600x + 85x^2 − x^3 − 160,000 dollars, selling how…

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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: Find the linear function that matches the table of values below. y -2 -1 -1 -4 1 -7 O f(x) = - 3x -…

A: To find the correct option

Q: (-1, xS-4 2) f(x) = {2x + 2,-4 0 -8 64-2

A: We have to find the graph of the given function

Q: Find the value of (A+ V)²(x² + x) with h=1.

A: To find the value of Δ+∇2x2+x with h=1.

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: Find the linearization at x = a. 1 f(x) = = 5 +3

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Q: find all possible functions with the givenderivative. y' = 3x2 + 2x - 1

A: Definition used -     Function from derivative -         f(x)=∫f'(x)dx

Q: Let f(x) = e2x (x² – 2x – 11). %3D -

A: Given function, f(x)=e2x(x2-2x-11)                 ....(1)

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

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Q: Suppose a firm’s profit function is given by π(q)=(1526*q-1*q^2 )-(1*q^2+11*q). What is the profit…

A: First, differentiate the profit function πq=1526q-q2-q2+11q with respect to q to maximize profit.…

Q: Are functions f(x) = x² – 2, g(x) = x² + 2x – 1 and h(x) = 2x² + 6x + 1 linearly dependent? If yes,…

A: Let f(x), g(x) and h(x) are linearly dependent.  So, we can write: Then we compare both sides

Q: y=4x

A: Linear function is given by equation y=4x. we have to show that value of y increases by 4 between…

Q: f(x) = x2 + 4x – 5, x < -2 -

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

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Q: Find the points of discontinuity for 3(х+2)2 x3 + 4x2 + x – 6 a) h(x) = 6х — х2 b) f(x): 9— х2 -

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Q: Find values of x where f(x)=2x3 – x +5 and g(x)=x2-8 have same slope.

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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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