(4b) 6. (20%) Find the Laplace Transform F(s) = of f(t) if f(t) = 1. Hence find (f(t)) F(s) = L (f(t)) = L (1) = ] e¯*f (t)dt = √ e¯™ª.1 dt = √ e™ªdt 0 d if (e') = e² dt { e'dt = e' (6a) (6b) (6c)

Q: Let f(e) = In[r*(z + 6}*(z° + 6)"] f'(x) =

A: Given: Now,         f'(x)=lnx4x+62x2+69'        =1x4x+62x2+69x4x+62x2+69'…

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A:

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A:

Q: 2. Let F(x) = x s sin (t2) dt. Find F'(x). (a) sin (x²) dx (b) sin (x²) (c) sin (x²) + C (d) 2x sin…

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Q: Given 9 (x) = S* t² cos(t)dt use FTC Part 1 to compute g' (x).

A:

Q: (11) Let G(x) = | a In(1+t²)dt. (a) Find G(1). (b) Find G'(1). (c) Find G"(1).

A: a) G(1)=0 b) G'(1)=piln(1+x^2)|x=1 G'(1)=pi ln(2) c) G''(x)=pi(1/(1+x^2))2x G''(1)=2pi/2 G"(1)=pi

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Q: tan x If h(x) Vt + vt dt, then find ht(x). 0,

A: We apply here Leibniz rule

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A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: 35. A particle travels along a curve y = f(x) as in Figure 15. Let L(t) be the particle's distance…

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Q: 1. Let A(x) = | e -tdt. (a) Sketch a graph of e-t and use your graph to illustrate what A(x)…

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Q: The graph of f is given to the right. Let g(x) = f(t) dt. (a) Find g(3). (b) Find g'(-2). (c) Find…

A: Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

Q: Suppose f(x) = [ 6t² /1+t° dt .

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Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

A: Let us answer above questions

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Q: Compute F'(x) for each of the following functions: (a) F(x)= | ecos(t) dt; 1 (b) F(x) = | Vĩ+tª dt;…

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Q: (11) Let G(x) = 1 In(1+t²)dt. (a) Find G(1).

A: Solution Given G(x)=∫1xπ ln(1+t2)dt.We need to find the G(1)