(b) compute an estimate of x(1) for the initial-value problem dx 1+x x(0) = -2 dt sin (t+1)'

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Q: ne hundredth derivative of p (x) (x + x³ + x')1º (1 + x² )11 (x³ + + x Justify ya

A: P(x) = (x+x5+x7 )10(1+x2 )11(x3+x5+x7) Here, (x+x5+x7)10  will have x70 as leading degree. (1+x2)11…

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: Find a function f(x) such that f'(x) = − 5eª + 3x and ƒ(0) : = f(x) = - 1

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Q: G(x) = cos osV5t) dt G'(x) =

A: Recall: Leibnitz Integral Rule:              ∂∂x∫a(x)b(x)f(x,t) dt=∫a(x)b(x)∂f(x,z)∂xdt…

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: Given the function f(x) = 1/2x4 – x3 – 2,

A: Given function is fx=12x4-x3-2     .....1

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A: The given function Pt=108t3-3t4 gives the number of people newly injected t days after the outbreak…

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Q: If F (x) = (t2) dt , then F' (4) = cos 0,

A: DUIS rule is used

Q: 1. Find the derivative dy/dx for each of the following. Simplify answers. (a) y = (3x* + 2)¯° (b) y…

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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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A: Given:Here A(x)=∫1xe-tdtTo find:a)sketch the graph of e-tb)find the value of A(2)c)find…

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Q: 8. Consider the function f(x) =6x5(x6+10)4 (a) Define u(x) = x6 + 10. Then calculate: u'(x) = (b)…

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Q: 1. a)∫9/x t^4 cos(t)dt f'(x)= b)∫x^2/1 ((t^2+3)/sin t)dt f'(x)=

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