Use Taylor's Theorem to obtain an upper bound for the error of the ap cos(0.6) 1 - (0.6)2 (0.6)4 ≈ 2! 4! R₁ ≤ R4 +

Q: 1 If y = V1-x then y' = 2/1-x

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Q: Use the Mean Value Theorem to show that 1+x 0.

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Q: Verify the Mean value Theorem for the function f(x) = 2x2 - 8z +6 on [1, 3]

A: f(x)=2x2-8x+6  on [1,3] conditions of mean value theorem: i) f(x) is continuous at (a,b) ii) f(x) is…

Q: Using Newton's interpolating polynomial of order 2, namely, bo +b,(x-x)+b,(x-x)(*-x) where x, = 0,…

A: Given:   Newton’s method for polynomial interpolation of order two is given as:…

Q: By the Existence and Uniqueness Theorem, the IVP y' + y = sin x x2 – 25' y(3) = 0 is guaranteed to…

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Q: Show that if f is analytic in a region G and if the range of f lies in a straight line, then f is…

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Q: True or False? If f (c) is a local min, then f"(c) must be positive.

A: the given statement is: If f (c) is a local min, then f"(c) must be positive. we have to determine…

Q: Find [F sec²x dx by using trapezoidal rule, Simpson’'s one third rule, Simpson’s three eight rule…

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Q: (d) Prore that the function f(x) =X is Continous but not unifomly Continous on the intenal

A: Use the  absolun delta definition for uniformly continuous

Q: Give relations of the first four central moments with the raw moments.

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Q: Show that Lindeberg's condition follows from Lyapounov's condition.

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