Let A (x) = = [² 501) 4321 34 f(t) dt for f(x) in the following figure. y=f(x) 1 2 3 4 Calculate A (0.5), A (4), A' (0.5), and A' (4).

Q: 2. . If f(x) dx = 4 and 3g(x) dx = -9, evaluate [² [3f(x) + g(x)] dx

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A: (a) fx=x-13x+4      fx=3x2+x-4 Product rule:     ddxu.v=uddxv+vddxu Let:     u=x-1v=3x+4 So,…

Q: 2 Find an x² x³ +3 anti-derivative for each of the following: for x³ +3>0 x + 2 x² + 4x² 5 a x² +1…

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Q: If f(x) = (x² – 9) (3x – 3), find the following a. f( – 1) = = 48 b. f'( – 1) = 0

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Q: Given h(x) = (-x² – 2x – 2), find h' (0)-

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Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 f'(2) = g'(2) =…

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Q: Let A(x) = 4 3 2 1 y f(t) dt for f(x) in the following figure. y = f(x) 1 2 3 4 Calculate A(0.5),…

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Q: Let f(1) = 2 and f (1) = 3. Suppose g(x) = [f(x)²=]. Calculate g' (1). %3D %3D

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Q: After being closed for approximately 18 months due to a pandemic, Disneyland re-opened to California…

A: Given that                                         N(t)=∫0tE(t)-L(t)dt where E(t) is rate at which…

Q: Let y be a function such that y(1) = -9/4 , where Y(s) = L {y (t)}. If it is known that:…

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Q: Calculate M6 for f(x) = 5 · In(æ³) over [1, 2].

A: Given:   f(x)=5.ln(x3) over [1,3]

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A: Given v(ψ)=VψVψi           (1) where Vψ=1-e-16π3ψ2 and Vψi=1-e-16π3ψi2 Since ψi≠ψ and ψi is the…

Q: Given g(z) = In(5z+), the derivative g (z) is. %3D O 42 O 5z +z O 20z +1 O 20z +1 5z4 +z 5z +I 20z+1

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Q: Exercise 4. Find the derivative of each of the following functions. a) f(x) = In((r³ + 1)e°) b) h(x)…

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