Let f(x) = 2 Using the centered 3-point formula for 1 derivatives: (x+1) f'(0) -0.502509 using h = 0.1 %3D f'(0) -0.500626 using h 0.05 Applying Richardson's extrapolation on the above values, we get a better approximation of f'(0) which is: O 0.234256 O -1.99985 O -0.499998 O 0.249999

Q: f(x) = e2 sin¯+(3x) + In (cosh-1(e³x))

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Q: The central difference approximation to the derivative ƒ(x) = x² sin(2x) at x = π/3 is: (use step…

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Q: The backward difference approximation to the derivative f(x) = x² sin(2x) at x = π/3 is: (use step…

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Q: f(t)=5 sec²(7 Tt – 3)

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Q: Find the derivative of the function given below. h(w) = 9w arcsin w h'(w) =|0

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Q: Compute the derivatives of the following functions using differentiation rules. (a) f(x) = *-3 + 1…

A: Here we will be using quotient rule in part a) product rule in part b) power and chain rule in c)

Q: The forward difference approximation to the derivative f(x) = x² sin(2x) at x = π/3 is: (use step…

A: The forward difference approximation to the derivative f(x) = x2 * sin(2x) at x= π/3 (use step size…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: