5. Given f(x)=vx+4 and g(x) = x² -5, find (f •g)(x) and (go f)(x) and the domain of each composition.

Q: 1/4 using the Linear Approximation L(x) of f(x) x14 at a = 16 Approximate 181/4 (Use symbolic…

A:

Q: 5. If f(x) = 2x² - 3 and g(x) = 2 sin x, determine (fog)(x) and (fog)(2), 0≤x≤ 2n.

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Q: Find the linearization L(x) of the function f(x) = x^3/4 at x=256.  L(x)=?

A:

Q: 15. With f(x) = 3x +1 and h(r) = 2x – 4, find (f oh)(5) - %3D

A: we know that  (fog)(x) = f (g(x))

Q: 13 Given that f(x)= 2x+1 and h(x)=x, find (h o f)(3).

A:

Q: If f(x, y) = 2x+6 (2a-6y) of then is given by:

A: In the above question we will take y as constant since we have to partially differentiate it with…

Q: Let h(x) = f(z) where f(x) = ln(3x² + 2x +2) and g(x) = -2x. What is h' (x)?

A: hx=fxgx=ln3x2+2x+2-2xf(x)=ln3x2+2x+2 Differentiate f with respect to x…

Q: 2. If f(x) = x - 3 and g(x) = x2 + x, what is the composition g(f(x))? a) x2 + x + 9 b) x2 - 5x…

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…

Q: 1. Find the composition function a) y =f(x) = b) y = f(x) = 2x + 5x2

A: a)  given   f(x) = 1x Thus composition function of f(x) = g(x) = f{f(x)} = 11x = x

Q: 2 Find [f(x) + 5g(x)]dx if 2 |f(x)dx = 8 and / g(x)dx = -1. -4 [f(x) + 5g(x)]dx = i -4

A:

Q: Find the linearization of y = eV3x at x = 64. (Use symbolic notation and fractions where needed.)…

A: Solution: The objective is to find linearization of the given function

Q: 5. If f(x) = 2x² - 3 and g(x) = 2 sinx, determine (fog)(x) and (fog) (), 0≤x≤ 2n.

A:

Q: 2. If f(x) = 1 + x², find fof 3.lf f(x) = -x, g(x) = 2x + 1 and h(x) = x², find fogoh,

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Q: find the interverse of the fuction f (x)= 2x + 3/x-4

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Q: Find the linearization of y = eV1x at x = 36. (Use symbolic notation and fractions where needed.)…

A: We have to find linearisation

Q: 2 If f(x) = and g(x) then (g of)(x) is equal to x + 3 1 + 3x A x + 3 D 2x x + 3 2х 1 + 3x 2x

A:

Q: 5. Suppose that f (x) dx = = 5, f (x) dx = -3, g(x) dx = -1, and g(x) dx = 2. Compute | (2f(2) –…

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Q: 2. If f(x) = x-1 and g(x) = - x2+ 2 a) Find (fog)(x)

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 38. f(x) = x² at x = -1 %3D

A: Solution Question 38 Given, The curve  fx=x2 We have to find the equation of the tangent at point x…

Q: dæ - x² – 10a – 21 -x – 3 - In x + 7 -æ – 3 -In +C +C x + 7 A x + 7 æ + 7 -In -x - 3 +C -In -x – 3…

A: Here we will solve the given intigral,

Q: 19. f(x) = x - 4, g(x) = Vx + 5, x 2 -5 %3D

A: Consider the functions f(x) = x – 4, g(x) = √(x + 5), x ≥ –5

Q: If f(x) =3 ln x and g(x) = e2 , find go f(x). %3D

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Q: Given f(x, y) = 4x°y+ 7xy*. Compute:

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Q: 6. If /f(2)dæ = (x + 5)*eª + ln(|æl) + C, what is f(x)?

A:

Q: Find the general Selution yer r the equatiJen S/0x)-14 ()+ 0 By(x) = =D0 dlax

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Q: In Problems 17–19, graph each function.

A: Points that lie on the curve helps to draw the function. Substitution of the arbitrary values of x…

Q: 4. If f(x) = -6x and g(x) = -6x %3D 203 2x+3 and g(x) = 3x 5. If h(x) = %3D

A: The solution are next step

Q: 0, x4. then P(2<X <4) is equal to

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: By= In(Cx-2)

A:

Q: 2. Let f(x) = 3x + 6 € Z7[x]. Find all associates of f(x).

A: The given function is fx=3x+6∈ℤ7x To find: the associates of f(x).

Q: 12. Find the general solution using Reduction of Order: a) y"= 2ln x b) y" + y' = cos 3x

A: We have to find the general solution: y''=2lnx. Here, the value of y1 is not given.

Q: 25. lim h→0 (x+h)² +4(x+h) —x²− 4 at h (A) x³ + x4 (B) x² + 4x (C) 2x+4 (D) nonexistent

A:

Q: 5. Show that the formula for the Secant method can be written in the form xn+1 = [f(xn)xn-1…

A: Secant Method: Consider, y = f (x). Let, x0 and x1 are two initial approximations for the roots of f…

Q: For y = In (x + 3x – - 9), to find y' would require the chain rule. If y = f(g(x)), find an f(x) and…

A: We have to find the derivative using chain rule

Q: 10. For f(x) = 2x3 + 7x + 4, g(x) = 4x? + 4x + 6, and h(x) = 6x² + 3 in Zg find f(x) + g(x)h(x) with…

A:

Q: and X4 %3D If the engine type is traditional, then x3 = When you plug in these two values in the…

A: When the qualitative predictor has m levels then we create (m-1) dummy variables. Here the…

Q: 12. Find the general solution using Reduction of Order: a) y" = 31n x

A:

Q: 6 4 Verify that for f(x, y) = 3x°y* - 4x°y°. дх ду ду дх of

A: Given problem:-

Q: 4. If the secant method is used on f(x) = x^5 +x^3 +3 and if x_(n-2) = 0 and x_(n-1) = 1, what is…

A: The given function is,

Q: Find the linearization L(x) of f (x)=- Vx -5 at a =3. – 5 2.

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Q: -5-k -5 If L f(x- k)dx = 1, compute f(x)dx. %3D 3-k 3

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Q: 29–44 Find the critical numbers of the function. 30. f(x) = x³ + 6x² – 15x

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Q: Let f(x) = x³ + 3x² - 24x + 1 and g(x) = x³ + 6x² − 36x + 1. Fo have critical points?

A: Given,            f(x)=x3+3x2-24x+1    and     g(x)=x3+6x2-36x+1

Q: 21 12 b. f(x) – f(x) = f(x) - where a= and b=

A: Suppose point c belongs to the interval [a, b], then ∫abfxdx=∫acfxdx+∫cbfxdx

Q: If g (x) =3x²– 4x+5 ; G(x)=x³– 2x²+ 5x , then G is the anitiderivative of f . A True B) False

A:

Q: Given f(x, y) = 6x²y – 5xy*. Compute:

A: This question is based on Partial differentiation.

Q: Find the linearization of y = eV3x у at x = 64. (Use symbolic notation and fractions where needed.)…

A: topic- linearization of a function

Q: 3. If f(x) = -x, g(x) = 2x + 1 and h(x) = x2, find fogoh 1 point %3D %3D О А. х2 - 1 О в. 2х2 - 1 О…

A: We use fogoh=f(g(h(x))).

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.