Let F(x)= f(x) + g(x)e* + h(x)e2x+C be the antiderivative of G(x) = (x+ e*)", Determine the value of (x) + g(x) + h(x) for x=6.2 (use 2 decimal places)

Q: Given that f(x) = V h(x) = x³ g(x) = = %3! Find (f ogo h)(x)

A: Composite functions concept is used.

Q: Let f(x) = (x³ + 3x + 7)3 f'(x) = f'(4) =

A: According to question given thatf(x)=(x3+3x+7)3

Q: Find f-1(x) f(x)=(e-x)/x

A: Given, f(x)=(e-x)/x To find f-1(x)

Q: Let f(x) = 2x e¯x*,x > 0 and Let Y x2. Find G(y)and g(y). %3D

A: In this question,  we need to transform the variable in the probability density function.

Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

A: We have the given function as fx=e-x22              ⋯⋯1 As we know that, a point of inflection of…

Q: f(x) = xe (1+e*)

A:

Q: Let f(x) = √√4x² 4x² + 3x + 5

A:

Q: fx) = (4x² + 3x"²) e*. %3D Do you think that the domain of f'(x) is the same as the domain of f(x)?…

A:

Q: Given f()= 2x + 1 and ()= r*+ 2x-1, fnd (f- (1).Then valute the difence when x=2.

A: Sum and difference of the two functions

Q: Let F(x) = f(x5) and G(x) = (ƒ(x))5 . You also know that a¹ = 14, ƒ(a) = 3, ƒ'(a) = 8, ƒ' (a³) = 6…

A: Use the following formulae, to obtain the solution. Chain rule for differentiation:…

Q: Let F(x) =Cx41D, fCx)=X,and gox)=x+1 True or fals e (gof)(x) = FCX).

A:

Q: Find f such that f'(x) = 9 √x f(9) = 59.

A: f′(x)=9x,f(9)=59

Q: Let f(x) = ln(x² + 2x + 6) f'(x) =

A: We have to find the derivative.

Q: Two triangles are____________ if the lengths of two corresponding sides are equal and the angles…

A:

Q: Differentiate y = In(x³ + e*) .2 3x+eX А. x3+e-X 3x2-ex В. x3 +e-X 3x2-e-x C. x3-e-X 3x2-e-x D.…

A:

Q: s defined by + x). The value o ind off to 1 decimal

A:

Q: Let p(x) = x³ - 17x² + 11x + 76. Compute p '(x) and use it to find all values of x for which p '(x)…

A:

Q: B) If fx) =-3x² +13 and g(x) =x'+8r-2; find the following. i) (g+f)(x) ii) Ax) - glr) C) 1) If f(x)…

A:

Q: Let F(x) = f(x5) and G(x) = (ƒ(x))5 . You also know that aª Then F'(a): = = = 8, f(a) = 2, ƒ'(a) =…

A:

Q: etx +1 Differentiate the function f(x) = In e* +1 O e*+1 4ex +1 4e4x ex etx +1 e* +1 4e4x ex etx +1…

A: Please see the explanation below

Q: lo UcE - Uxx=0 4(x,0) = f(x) 4= (x2,0) = g(x)

A:

Q: Let f(x) = = f'(x) = = /3x² + 3x + 2 2

A: