Evaluate L 1 s(s²+4) of the Convolution Theorem. by using the Inverse form L{f*g} = L{f(t) }L{g(t) }=F(s) G(s) (Convolution Theorem)

Q: If f and g are differentiable at a , then f (x) + 4g (x) = I (x) + g (x)]. True False

A: Here, the given statement is  If f and g are differentiable at a, then ddxf(x)+ddxg(x)=ddxf(x)+g(x)

Q: 1 >Use the following models to consider the function f(x)=; on the interval 1+x? [-5,5]. (1)…

A: The function given is as follows: fx=11+x2 (1) We are asked to find the interpolating polynomial of…

Q: Can you please find (f o g o h)(x) where f, g and h are defined, and it's in the attached picture.…

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Q: Find (a) the domain of  f and (b) f-1 and its domain.   f(x)  = In  (2 + In x)

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Q: Use appropriate Lagrange interpolating polynomials to approximate f(1) if f(0) = 0, f(2) = −1, f(3)…

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Q: (iii) Find f' and state its domain.

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Q: Prove that: g(x)Vf(x) – f(x)Vg(x) (@)V %3D g(x), a* + (a? + 1)²a** g(x)g(x – 1) | -对tre (b)A² %3D…

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Q: 3.x2 Let g(x) = 9. x > 0 -2x2 x <0 (a) Prove that g is differentiable on R.

A: A f(x) function f is differentiable at x iflim h→0 f(x+h)−f(x)h exists. i.e. if lim h→0+…

Q: Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 3x + 1. 1 h(x) = V3x + 1 f(x) =D

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Q: If g'(0) = 7 and f(x) = 2g(x) - 4ex - x² + 3x, what is f'(0) [A] 13 [B] 11 [C] 14 [E] 17-4e [D] 17-e

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Q: What is the function's end behavior? f(x) =x-3x3 +x - 3 Select all that apply. A → + 00, as x→ + 00…

A: We have to find the option

Q: If f(x) = x + 7 and g(x) = x - 7, (a) f(g(x)) (b) g(f(x)) = (c) Thus g(x) is called an - Question…

A: given f(x)=x+7 and g(x)=x-7

Q: Differentiate. y =x° In x- dy II

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Q: Let x) = (x+3)³ +2 The graph of the inverse function y = f¯¹(x) has a vertical tangent at: (Hint:…

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Q: Consider the two functions. f(x)=2x-(3)/(2) g(x)=2x+3 Which translation maps f(x) onto g(x) ?

A: A translation is a geometric transformation that moves every point of a figure, shape or space by…

Q: Let f(x) = 4x- 1, h(x)= -x+1. %D Find (f o h)(3). (f o h){3} =] %3D

A: Composite function  foh (x) is given by  foh(x) = f(h(x))

Q: consider the functions f (x) =5/x and g(x)= x/x+2 A) evaluate and smiplify (f+g)(x) and state the…

A: fx=5x,  gx=xx+2 f+gx=fx+gx f+gx=5x+xx+2 f+gx=5x+2xx+2+x2xx+2 f+gx=5x+2+x2xx+2 f+gx=5x+10+x2xx+2…

Q: g(x)= f (x)-(f(x))" +(f (x))* for all xeR. Prove that f (x) and g(x) increase or decrease together.

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Q: Q8. Given f(x) x + 2 if x >1 2x 1 if x< 1 (a) Determine f-(2,4)).Then discuss the continuity of…

A: 1) Here,  y=x+2, if x≥1⇒y≥3So, f-1(x)=x-2 if x≥1 So, f-1(2)=2-2=0So, f-1(2,4)=0 Now, f is not a…

Q: Discuss the monotonicity of g (x), where g(x) = 2f + f(6-x) for all x e R. 2

A: Test for monotonicity:           let us consider a function is continuous on [a ,b] and it is…

Q: f(x) = x²e*

A: Here we have to determine the inflection points of f(x). Givne:- f(x)=x2ex Differentiate with…

Q: The Function f(x) = sin( 2")- sin( 2 *) is %3D Select one: O An even Function O An odd Function O…

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