2. Verify that f has an inverse and find (f-1)'(c) f (x) — 1 — 2х — х3, с — 4 [Hint: Find f1(4) using graph]

Q: B) Estimate the next root of the function f(x)=x^3-x-1 using Muller method, let x0=1, x1=2, x2=1.5

A: Muller method: The Muller approach is applicable to any root-finding programme, but it is especially…

Q: 13. If f(x) = 1 / (5 + 7x) , find S f(x) by using a u-substitution. Show the u-substitutions.

A: Given, fx = 15 +7x  We have to find ∫fx using u substitution

Q: Find f(x) if f°(x)=cos x with f(0) =1, f'(0) = 2 , and f'(-)=3.

A: Keep on integrating we are end up with an answer. For those constants we need these initial…

Q: The function f(x) = 3x³ + cos(3ræ) + 2x , x > 1 is known to be a strictly increasing function on its…

A: Given f(x) = 3x3 + cos(3πx) + 2x,  x≥1   ⇒ f'(x) = 9x2 - 3πsin(3πx) + 2

Q: 8. If g(x) = e*In(x+1), compute g'(x). What techniques are you using in this case?

A: Solution is given below..

Q: Let f(x) = V5x + 4. Compute (f-1)'(2) using the Derivative of an Inverse Function Theorem.

A: Solution

Q: Z→ Z be such that f(x) = 4x + 2. Is f invertible, and if so, find its inverse function.

A: Given query is to find the inverse function.

Q: Sketch a graph of the function f(x) 2 sin(2x). %3D -77/8-31/4-5n/8-/2 -3/8-7/4-T/8 t/4 3n/8- /25/8…

A: Given function is f(x)=-2sin(2x)We know that period of sin(x)=2πThe period of sin(2x) will be π and…

Q: find the inverse of th functien y=In(x_z). 2)

A: The easiest way to find the inverse of a function is to swap x and y and solve for y.

Q: a2f b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D f(x,y) = In/x2 +…

A: The first step inludes the  partial differentiation of the functions individually with respect to y…

Q: Prove that converting the Higher-Order derivatives to the finite difference formula would be: f(x;)…

A: Solution: (1) f''xi=fxi-2fxi-1+fxi-2∆x2 We know that f'xi=fxi-fxi-1∆x ......(1) Then,…

Q: Suppose the nonzero function f(x) is infinitely differentiable and that f'(x) = -3f(x) for all a…

A:

Q: Assume that the function f defined by f(x) = 5x+ sin(Tx) is strictly increasing on R and find…

A:

Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

A:

Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: Prove that 1 3V2 dx < 3 + x (Hint: Theorem 5.9(ii) and carefully chosen functions should do the…

A:

Q: Find the roots of the function f(x)=(2x-1)(x2+2x-3) with x belong to R

A: f(x)=(2x-1)(x2+2x-3)=0 We have find all the real numbers that make f(x)=0 because it is given that x…

Q: 1. Consider finding the root of f(x) =x´ – 5 use secant method, ɛ = 0, and start with the a interval…

A: given , f(x) =x2 - 5  we have to find roots of f(x) in interval by using secant method

Q: Suppose f(x) = – 2x – cos r. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

A:

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A:

Q: 2. Find the linearization L(x) of f(x) = x³ - 2x + 3 at x = 2 and use it to approximate f(1.9) and…

A:

Q: 1. Use the limit definition of the derivative to find g'(x) if g(x) = 2x² – 6x + 13.

A:

Q: Compute the resulting error in the function f (x) = x³ for value x = 2.38 with an error Ax = 0.005.

A:

Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

A:

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: Suppose that f and g are discontinuous at x = c. Does it follow that f + g is discontinuous at x =…

A: Let us define that Then both f and g are discontinuous at x=2

Q: 12. Use the definition of increasing to argue that f(x) = x5 is increasing on all of R. Then use…

A: The increasing of a function indicates that the value of the function increases with the increase of…

Q: Consider the function f : RH→ R defined by f(x) = 2e(2z+5) log(2r+5) + If f convex or concave ? Why…

A:

Q: Calculate the  M6  approximation for  f(x) = 4(x + 18)  on  [5, 8].   M6 =

A:

Q: u² -v² +uv x=In", y=' (11–v)-

A: two functions x=lnuv...........(i) and y=u2-v2+uv(u-v)2..........(ii) are given. To find the…

Q: Find the best quadratic approximation to f on the interval [ 0, 1].                     f(x) = x3

A:

Q: 5. Show that the function f (x) has roots between (0,2) x + 2x – 3 f(x) = %3D x – 1

A: Given that: f(x)=x2+2x-3x-1

Q: 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif-…

A: The Complex Derivative Definition: Let f be a function defined on a neighborhood of z0 ∈ ℂ. If…

Q: Find the dérivative of the function: f(x)=In(e^x-13x)

A:

Q: Prove that f (x) = x2 takes on the value 0.5 in the interval [0, 1].

A: Here given

Q: Prove that f(x) = tan(x) is never negative in 0 < x < ; and show that g(x) = x=l sin x decreases…

A: We have to prove that f(x)=tan(x) is never negative in the interval 0,π2. Then we have to show that…

Q: Q3: a) Let f : Z → Z be such that f(x) = Vx² – x + 1. If invertible, and if it is, what is its -…

A: the function is invertible if its one -one and onto. The function is one - one if f(x1)=f(x2)…

Q: Derive a numerical differentiation formula of order O(h4) by applying Richard- 4. extrapolation to…

A: Its given that:

Q: Suppose h(x) = [,f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) -4-…

A:

Q: 1. Use the definition of the derivative of complex function to show that f(z) is not differentiable…

A: We will show the given statement.

Q: 6. Prove that the function f defined by f (x)= ,xe(-00,1), has an inverse function 1-x defined on…

A:

Q: Find all the x-intercepts of f(x)=cos(x) on the interval [0,2π)

A:

Q: Find f(x) if f(3) = 0 and the tangent line at (x, f(x)) has slope x2 + 5 In (14) f(x) =| 히n 글미(구+ 5)…

A:

Q: C. Show that f(x) = (x26)² has no inverse on the interval (-∞,0).

A: Since you posted two questions here, i can answer only 1. Please reupload second question again.…

Q: , for x 1 Let f(x) be a function defined by f(x)=- Discuss the contuniuty of f and f'.

A:

Q: Find an approximation that is accurate to three decimal places to the zero of f (x) = x³ -3x- 1 in…

A:

Q: Use differentials and the graph of f to approximate    (a) f (1.9) and (b) f (2.04).

A:

Q: Approximate the value of f"(2.156) if f(x) = 2tan(x) + %3D cos(2x). h = 0.003 %3D O -18.22610955 O…

A: Here the given function is f(x) = 2tan(x) + cos(2x)

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.