Show that the third derivatives with extended step size h is given as follows: ƒ™(x) = S(x−3h)−6ƒ (x−2h)+12ƒ (x−h)−10ƒ (x)+3ƒ (x+h) +0(h²) 2h³ where O(³) is the truncation error of the approximation. State your assumption(s).

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Find the derivative. y=(x2+x)-3 OA. dy 3x5 (2-x³) dx (1+x³)3 OB. dy_3x4 (2-x³) (1+x³)3 dx 5C 31 ...

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Q: Find the second, third, and fourth order derivatives of: y= f(x )= ax7 + bx3 + c y= f(x) = 3x/1-x…

A: It is simple derivative

Q: Which among the graphs is more convenient to use? BAR GRAPH or PIE GRAPH?

A: Pie graph become confusing when there are many distributions. Also, it becomes very difficult to…

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: Find the derivative of y with respect to x. y = cos1 (5x2 + 4) 10x + (5x2 + 4)2 -10x Vi- (5x2 + 4)?…

A: The given function is  y= cos-1(5x2+4)  We have to find the derivative of this function w.r.t. x

Q: Determine the derivative of the following functions using chain rule. 3 * 1. f (x) = (2x² – 2x + 1)…

A: 1.f(x)=(2x2-2x+1)3 2. f(x)=5x3-8x2+9x-6

Q: 2. Determine the derivative of g(t) = 8°[(2t + 1)² + t].

A: Given that     g(t) = 8t[(2t+1)2+t]

Q: I. Find the derivative of the following. Show that the applicable differentiat rules has been used.…

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Q: Find the derivative of the function f(x) = – 2x1 + 5x – 7. A. -2x + 5 C. -2x? + 5 E. None of these…

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Q: Suppose a and b are +ve integers with d=gcd(a,b) prove that gcd(a/g,b/g)=1

A: # The statement should be gcd(a/d, b/d) =1 instead of gcd(a/g, b/g) =1 Given that d=gcda,b let…

Q: 3. Find the second derivative of f(x) = 2sin²(3x) а. 36сos? (3x) — 36sin? (3x) b. 36сos (3x) —…

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Q: i. ii. following functions. y = 6x² 10x - 5x-² V= 1+x-4√x x

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Q: Use the rules for derivatives to find the derivative of each function defined as follows.     We'll…

A: 38.40.50.

Q: The sign x (t) is even symmetric and the sign y (t) is equal to the derivative of x (t). Show that…

A: even symmetric means it satisfies x(t)= x(-t) while odd symmetric means it satisfies x(-t)= -x(t)

Q: The derivative of y = sin(e2x) is: 1. e2xcos(e2x) 2. 2cos(e2x) 3. 2e2xcos(e2x) 4. 2xcos(e2x)

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Q: Find the derivative of y = f(r) = VI(3r + ²). x(3x+x %3D

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

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Q: I. Find the derivatives of the following functions: 4. -3xy? + 5x²y² = 2x² %3D

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