1 s(s² +9) of the Convolution Theorem. Evaluate L by using the Inverse form L{f*g}=L{f(t)}L{g(t)}=F(s) G(s) (Convolution Theorem)

Q: x(x2 – 1) x2 +1 63. GU Let h(x) and the increasing/decreasing behavior of f. Sketch a plausible…

A: We use a graphing calculator to graph h(x)

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: (a) Evaluate f(g(a)).

A: Given graph of f and g,

Q: Consider the function f(x) the difference quotient = 7 x²+1/ 3 4 -X-2. Compute f(xo+h)-f(xo) h

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Q: (x- 1) (x– 2)(x+ 1) (x+ 2)(x- 3) (x+ 3) 2. Let f"(x) = and g'(x) = For what values of x are Az) and…

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

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Q: f(x) || 1 x² + 1

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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: x Find the natural domain of the function f defined by f(x, y) = and /25 - x² - y² draw a sketch of…

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Q: Find  f ∘ g ∘ h. f(x) = 1/x ,  g(x) = x3,   h(x) = x + 4

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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 G be a direct product of H and k product of 2 (H) 'and z (k) then Z(G) is a direct

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Q: 25 – 3 Evaluate the domain of the function h(z) = 3 - z2 - i

A: The domain of a complex function f(z), is the values of z for which the function is defined .

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

A: The given inverse Laplace transform is .To evaluate the inverse Laplace using the Inverse form of…

Q: Consider the function below. f(x, y) = In(x + y - 3) (a) Evaluate f(1, 3). (b) Evaluate f(e, 3) (c)…

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Q: The function h(x) is defined as: = 1 x+5 can be expressed in the form f(g(x)), where g(x) = (x + 5),…

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Q: x + 5 Consider g(x) : on the interval [1,4]. Show that g(1) 0. Explain why, in this case, it is NOT…

A: Let the function is gx=x+5x-2  on the interval [1, 4] To find the value of g(1) plug x = 1 in the…

Q: ak If h(x) = , show that h(k) – h(a) = h () .

A: We have to prove the given function

Q: Define (i) "f(x) is 0(g(x))", (ii) "f(x) is N(g(x))" and (ii) "f(x) is O(g(x))" Using the definition…

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Q: (x) = x. What is g(x)? g(x)- (1,5) 15 f(x)

A: As per given by the question, there are given that; fx=x2, then find gx. There are also given that,…

Q: Prove that, if f(x) and g(x) are any functions of x, (i (i (ii. f(x) 8 (x) A f(x) - f(x) A g(x) (iv)…

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Q: Solve the following IVPS using LT method. y" – 2y' + y = 8(t – 1) y(0) = 3, y'(0) = -4. |

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Q: escribe the transformations on the cubic function (x) = ¹/2 [5(x + 2)]³ - 3

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Q: Find all points of inflection of f (x) = In(1 + x²) O -1, In2), (1, In2) O (-1/sqrt(2), In(3/2)),…

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Q: Find domain of the function f(x) = %3D (a) R (b) R-(9). (c) [9,00) (d) (9,00)

A: Domain is the set of all values of x for which the function is defined. That is, all values of x for…