(a) Develop a first-order method for approximating f" (x) which uses the data f (x – 4h), f (x + 3h), ƒ (x) and f (x + 4h). (b) Using the most accurate centered difference formula, approximate f" (1) and then state the error in the approximation, given f (r) = sin (x) + , for each he {0.1,0.01, 0.001}. Use an accuracy of 6 digits throughout.

Q: f(t) = u(t)+ (sint- 1) u(t- -))-(sint + 1). 미t +u(t – 27) %3D

A:

Q: derivatives of the following functions.   a)      exp(3x2)

A: a) Given function is e3x2.

Q: 1. Determine the slope of the following functions. į. f(x) = 4x³ + 5x4 - 9x + 2 f(x) = sin(3x) - 5x³…

A: We determine the slope of the following functions.                          i. f(x) = 4x3 + 5x4 - 9x…

Q: Find the derivative of the function. f(t) = (7t² - 4t + 1)3/2 21t – 6 f 't) = 7? – 41+ 1)² (72 – 4t…

A:

Q: 2. Find the anti-derivative of a. f(x) = 2x¹ - 5√√x³7−2e* ++ 3 1 1+x²

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: (2x + 3)4 (5x + 1)(x² + 3) y = (3х — 1)3, Find the derivative of the function x3 + 4 A. dy dx (2x+3)…

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Q: A2) Find the derivative of the following functions: x2 + 2 (a). f(x) x2 – 2 (b). f(x) = 2 tan-1(x) –…

A:

Q: 3) Find the following derivatives: a. y = 2x b. f(x) = 4x³10x² + 7x-15 c. g(x) = 3x(x² - 4)5 d. y =…

A:

Q: Find the derivative of y with respect to the appropriate variable. y=cosh ¹2√√x+10 O A. B. O C. O D.…

A:

Q: Let f(x) = 2x³ − ²x² – 3 1. Find the first derivative of the function. (This function can be easily…

A: given  f(x)=2x3-12x2-3

Q: 7. Draw the function (f(x) = cosx sin (x) and its derivative in one graph for the same range for x…

A: The objective is to solve the above questions.

Q: f (1, 2) = 3 and the derivative of the function f at the point (1, 2) in the direction of i + j is…

A: Given that, f(1,2)=3 The direction is i+j. And the distance is 0.7.