The acceleration of a particle as it moves along a straight line is given by a-21 -1. Ifs 1 and y- 2 when t-0, determine the particle's velocity and position when t-6s . Also, determine the total distance the particle travels during this time period.

Q: (b) Differentiate the function below with respect to a. f(x)=ln (22²+5x-7)

A: We have to differentiate the given function f(x) with respect to x. We will apply chain rule here.

Q: QUESTION 3 2²f дудх Round your answer to 4 digits after the decimal sign. Find the value of at (2,1)…

A:

Q: Problem #11: Let f(x) Find f"(In 2) (A) - (B) (C) (D)- (E) (Đ © H) - Problem #11: Select v

A: topic - functions and derivatives    Option H  f(ln2) =-6/343

Q: Let f (x) = x° + x³ + x . Find (f -1)' (a) for a = 3. O (s -1)'(3) = } . O (s -1)'(3) = } . O (s…

A:

Q: 16. Which of the following does NOT show that f and g are inverse functions of each other? (1 Point)…

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Q: 8. Is the following function analytical? f(z) = 2² - z²

A: Approach to solving the question:Rational Detailed explanation:The given function is:…

Q: 5 Suppose is the inverse of a differentiable function f, and let G(z) 1/f-¹(a). If f(4)-5 and…

A:

Q: x3-1 si x + 1 x4-1 f (x) = Determine whether the following Function 9.- %3D 1 si x = 1 b) Is…

A:

Q: • 61. f(x) = 4 – x², x2

A:

Q: 4. Let function f: R → R and function g: R → R be two functions for which f(g(x)) = x and g(f(x)) =…

A: We have to prove given statement.

Q: 6. The function f(x) is created by doing a horizontal compression of 3 on g(x). If (7, 3) is a…

A: horizontal compression means horizontal stretch.

Q: State if the following functions are even or odd and show why they are even or odd by using a…

A: Given: y=x2+4

Q: the inverse function of f(x) = ax is x+c hat is the value of a + b + c? +C= f-¹(x)= 8x - 7 .-x+3'

A: Topic:- algebra and calculus

Q: 11. Let f(x) = x³ - 2x² + x-1 so f(1) = -1 and f(2)= 1. Let g be the X inverse of f; that is, g(x) =…

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Q: ). Prove that the derivative of an even function is odd and that the derivative of an odd function…

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Q: 5. If Mo is the mode of all original observations and we add any constant to all original…

A: Given that  We have to determine the given statement is true or false.

Q: Function g: R → R, defined by g(x) = x" +5 is a one-to-one function. O True O False QUESTION 8…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.