Are functions f(x) = x² – 2, g(x) = x² + 2x – 1 and h(x) = 2x² + 6x + 1 linearly dependent? If yes, write f(x) as a linear combination of g(x) and h(x).

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

A:

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: Find the linearization of-ƒ(x, y) = x2 - xy + 1- 2 y2 + 3?

A: Here we have,  f(x,y) = x2-xy+1-12y2+3 at (3,2)

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

A: f(x)=∫0xt3+2t2+2dt

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

A:

Q: Find the linearization of the function at a . f(x) = x 4 + 3 x2    , a = -1

A: We know that ,The linearization of the function at v=ais given by fa+f'ax-a

Q: 2) Find the fixed point of the functions : A. f(x) = x² + 5x + 3 B. f(x) = x³ – 4x² + 6x – 2 C. f(x)…

A:

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

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 & f2=1

Q: 1, Differentiate the function. (2) f(x)= 5x² – x+1 (3) f(x)= (2+3x'j - nx (4) f(x)= e (5) f(x)= (x³…

A:

Q: what is the gradient of y=x3-3x2 +5 when x=1

A: Given y=x3-3x2 +5

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: If f (x) = x* and g(x) = x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule %3| multiplies…

A: It is given fx=x4, gx=x3, f'(x)=4x3 and g'(x)=3x2.

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

A:

Q: Find the maximum and minimum values of the 2x3 function f(x,y) = * - 2xy – 5x + 2y² + 4y + – 2xy –…

A:

Q: b- Determine the critical point of the function f(x) = x5 – 5x* + 5x³ –- 1 %3D

A:

Q: The linear functions m(x) and n(x) are perpendicular to each other and intersect on the x-axis. If…

A: Two lines with slope m1 and m2 are perpendicular to each other if m1m2=-1 Given: m(x)=4x+48 Let the…

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

A: fx=x+4

Q: Find the linearization of the function at a . f(x) =  x3/4    , a = 16

A:

Q: 1) Determine if the two functions are Linearly Dependent or Linearly Independent. g(x)= 2x – 4 f(x)=…

A: Given: f(x)=2x+4 g(x)=2x-4

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: Find the maximum and minimum values of f(x, y)=x+3xy2-3x2-3y²+4.

A:

Q: Differentiate the function (use chain rule): y = 2x2 /x+1

A: as per our guidelines, we are supposed to answer only the first question in the serial number.

Q: I Eliminate the arbitrary constants y = x²+ ax + be*

A:

Q: Linearize f(x) = (x2 - 3x + 3)2.1 near x = 3. %3D

A: Consider the function  f(x)=x2−3x+32.1

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

A:

Q: Find the linearization L(x) of the function at a. f(x) = x4 + 6x2, a = −1

A:

Q: ATTACHED THANKYOU

A: Given that the first term of the AP is a and common difference is d.And the AP is constructed by the…

Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

A:

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

A:

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: Find the linearzation L(x) of f(x)= \sqrt(5x+16) at a=0

A: Given Fx=5x+16 at a=0The objective is to find the linearzatin Lx ofFx=5x+16 at a=0find the…

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

A:

Q: Find the linearization L(x) of y = (64+3x2)-1/2 at a = 0. L(x) = %3D

A: The given function is: y=f(x)=(64+3x2)-12 So, f'(x)=-1264+3x2-32(6x)        =-3x64+3x232

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

A:

Q: How do you linearize a function ƒ(x, y) of two independent variables at a point (x0, y0)? Why might…

A:

Q: Find the linearization of f(x) = V16 – x² at a = 3. %3D

A: Given: The formula used for linearization:

Q: Compute f(c + h) – f(c) at the indicated point. f(x) = 7x²; c = 5

A:

Q: Find f, (x.y) if f(x.y) = x² - 7xy – 9y². (x.y) =|

A:

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

A: The given equation is ax2+bx+c=0.

Q: Find the general solution of y" = 6y' – 9y where y is a function of x.

A: Given differential equation, y''=6y'-9y Find the general solution of the differential equation.

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

A:

Q: eliminate the arbitrary constant for: y=c_1 x^2+c_2 e^2x

A: y=c1x2+c2e2x                                                           (1) On differentiating both…

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

A:

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

A:

Q: find the maximum and minimum values of f(x,y)=x3+3xy2-3x2-3y2+4

A:

Q: Find the maximum and minimum points of f(x) = x(12 – x)?

A: topic - application of derivatives

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

A:

Q: If f(x)=x* and g(x)= x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule multiplies derivatives to…

A: