We consider the example from class for approximating f'(2) for f(x) = sin(x) using a finite difference approximation. This time, we will be using f(xo+h)-f(ro-h) 2h f'(xo)≈ instead. Show using Taylor's Theorem that you expect the truncation error of this approxi- mation to be O(h²).

Q: Given f(x) f''(x) = = = √²* (t³3 + 4t² + 6) dt, 0 (t³ + 4t² + 6) dt, answer the follow

A:

Q: Find the perpendicular distance between tangent line to the curve f(x) = ln(sin(x)) when it has a…

A: Given,f(x) = In (sin(x))To find prependicular distance between,tangent line to f(x) at slope = 3 (0…

Q: Suppose that f (0) = 2 and f'(x) 0. Show that f(4) 0.

A: f(0)=2   and f'(x)≤3  for all x>0 ⋯(i)integrate (i) w.r.to x ,we getf(x)≤3x+kput…

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: Suppose, f'(x)=2cosx+ sec x, -7<x<7½, and it is known that f(T) =D4. Find the function f(x). IT

A: Integrating on both sides, we get

Q: Explain why f(x + h) – f(x - h) 2h should give a reasonable approximation of f'(x) when f'(x) exists…

A: Explain why fx+h-fx-h2h should give a reasonable approximation of f'(x) when f'(x) exists and h is…

Q: Use the rule for square roots: f'(x) 2/ F(x) V F(x) to find the following derivatives (quickly d V…

A:

Q: 3. Suppose that f'(x)= sin(x) + tx² and that f(T) = 0. Find f(x).

A: Given f'(x)=sin(x)+1/√x+ x2 and f(π)=0

Q: For the function f(x)=3x² - 2x+7, find f''(x). Then find f’’(0) and f’’(8). f''(x)=(Simplify your…

A: See this solution in below.

Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

Q: Consider f(x) = 3X. What is the best approximation for f'(2)?

A:

Q: Apply the method of Example 6 to f (x) = sin x to determine f ' ( π/4 ) accurately to four decimal…

A: Given function is fx=sinx. To determine f'π4. Solution: Function is fx=sinx. Differentiating the…

Q: Find f    if  f'(x) = 7x9 − 5 √x + 3 sin x,   f(0) = 4

A:

Q: Show that the error terms to approximate f'(x) i is and x-3h. --/h²f"(c) where c lies between x-h

A: To prove that the error terms to approximate f'(x) is -12h2f'''(c) where c lies between x-h and…

Q: The folowing is a reworded question from very last night . A printed solution of  a length of curve…

A: To find the correct integrand to evaluate the length

Q: mula for the derivative of the inverse function of f?

A: We have given a function  f(x)=∫0x(1+sin(sin(t)))dt We have to find f-1'(0).

Q: Let f(x) = x²+ Ax + B. By knowing that f(1) = 5 and f'(1) = 5, find the values for A and B.

A:

Q: Find f'(x) and simplify. f(x) = (0.2x + 2)(0.6x - 9) Which of the following shows the correct…

A: f(x)= (0.2x+2)(0.6x-9)

Q: Define f = sin(px^3)+cos(qx)^2 as a function of x (with p and q constant) and differentiate with…

A: see 2nd step.

Q: Slove: √x12 - X=0 it there there are multiple solutions. list them separated by a 2. Comma . X= eg.…

A: We need to solve the equation: x+2-x=0. An extraneous root is one that is derived by solving an…

Q: Find the general form of f if f'(x) = 5f(x).

A:

Q: Use the rule for recipocals : f '(x) f?(x) d 1 dx [ f(x) to find the following derivatives…

A: Given: Reciprocal Rule: ddx1f(x)=−f'(x)f2(x) Find: 1)  ddx1x2+2x+1=?2)  ddx1sinx+ex=?3)  ddxπx+1=?

Q: Let f (x) = 5x4 + 3x3 + 3x2 + 5x + 5. Fill in the missing coefficients for the derivative of f:

A:

Q: Use this definition to find f'(a) at the given number a. f(x) = V3x + 1, a = 8

A: