The two point backward difference formula to approximate f' (xp) with h> 0 is fixo + h) – f'xx) -h f(xo) – f(xo – h) h f(xo) – f(xo – h) -h O None of these fixo +h) – fíxq) h

Q: at point x0=1 ,x1=1 and x2=2 f(x)=sin(x)+(x^2)+xe^2 function crossing second Write down the…

A:

Q: Prove that f(x)= 2x-tan^1x-ln(x+√x^2+1) increasing on [0, infinity]

A:

Q: -х- 2, х<-1 -1, f(x) =. -1sx< 0 at x = -1, 1, 0 sin(2tX), 0<x<1 X, 1s x

A:

Q: The tangent line to y=f(x)y=f(x) at (−3,−2)(−3,−2) passes through the point (−4,−3)(−4,−3). Compute…

A:

Q: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

A:

Q: Sketch the graph of f (x) = sin x on [0, π,] and guess the value of f ' (π,/2). Then calculate the…

A: Plotting: y=sinx, 0≤ x≤ π

Q: Q7 Show that f is continuous on (-∞, 0) sinxif x - 4

A: Trigonometric function with sine and cosine in continuous in its domain.    Here in this question,…

Q: 2. If f(x) = cos2x, find f(0), f(--).f),f(-x) 3. If f(x) = x(x+1), show that f(x+h)– f(x)= h(2x +1+…

A: 2. f(x) = cos2x , find f(0) , f(-π/4), f(7π/8) ,                                         f(-x). f(0)…

Q: Show that the function f (x) is continuous on Sin x, r 4 -

A: You have to find the left and right hand limit for the given function.

Q: the

A:

Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

A:

Q: verify mean value theorem for the function f(x)=4x3 over ihe interval [0,2 ]?

A: verify mean value theorem for the function f(x)=4x3 over ihe interval [0,2 ]

Q: Find the absolute extremum point(s) of f(x) = e' -Cos x on [-골, T), E any.

A:

Q: Find a finite difference approximation to f"(x) using the points x — x − 2h, x-h, x,x+h,x+2h and…

A:

Q: 2) Use Newton's method to approximate the zero in f(x) = - x3 + 3x-x + 1, or explain why Newton's…

A: Consider the given function,

Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution: f:[a,b]→ℝ is differentiable at x0(a,b). Let us take upper derivative at x0+. Then,…

Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: Determine whether f(x) is differentiable at x = 0. Show your work. sin(x) cos(x)-1 3x + 1 f(x): = if…

A:

Q: Find the indefinite integral and check the result by differentiation. dt F--3-3)- 8. 12

A:

Q: 11. Determine the absolute extreme values of the function fx) = 2 cosx- x on the interval 0<x<2x.

A: We are authorized to solve only 1 question, please repost remaining Extrema

Q: 1 Differentiate f(æ) = sin-(4x). Use exact values. = (x),f

A: We use the chain rule for differentiation

Q: Q: Show that the function f(x)=- x sin ,X =0 is continuous at x = 0.

A:

Q: Use Secant method to find the root ofthe function:f(x) = 3x + sin x- e to 5 decimal places. Work…

A:

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: Let f(x)= x2 + sin x - 2 cos 2x. Find (f-1)'(-2)

A: Given: fx=x2+sinx-2cos2x To find: f-1'-2 Now, we know that f-1x' = 1f'f-1x

Q: Use second derivative test, If f(x) = - 4x + 10 then f(x) has a local maximum at the point 3 %3D O r…

A: here we need to find the point at which the function has a local maxima. the solution is following.

Q: Suppose /has a continuous derivative on the interval [0, 6]. Assume also that f' is increasing on…

A:

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1 Construct a Langrange Interpolating polynomial of…

A: The given question is solved below

Q: Find and locate the local and absolute extreme values of f(x) = x+(sin2x) in [0, π].

A: Find and locate the local and absolute extreme values of f(x) = x+(sin2x)in [0, π].

Q: What are the intervals of monotonicity of f(x) = arctan (2(x-1)) - ln IxI ?

A:

Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: Find the root between [-1,0] where f (x) = (x+2)³ +2x – 5 with error epsilon=0.1 by using False…

A: The false position method is one of the methods used to find the approximate root of a function in a…

Q: The approximation of the root x of the function f(x) = -x + sinx-2 accurate to within 103 using…

A:

Q: 5. Use the forward and backward difference approximations of 0(h), and a centered sin(x) difference…

A:

Q: Suppose (-8, 6) is a critical point of a function f with continuous second derivatives. If fra (-8,…

A:

Q: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

A:

Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

A: Given problem:- A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f,…

Q: Use Secant Method to calculate the root of a function f(x) = e-*(3.2sinx – 0.5cosx) on the interval…

A: To use decant method to calculate the root of a function

Q: Can i get help step by step with this problem?

A: Left side has integral. So to simplify we differentiate the right side.Answer(a): B)…

Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: 13 Use the Linear Approximation to estimate Af for f(x): when a = 2 and Ax = 2+x %3D (Use decimal…

A:

Q: find the most general ntiderivative f(x) = 4 sec2(x) + 3 sec x tan x

A:

Q: The tangent line to y=f(x) at (−8,−5) passes through the point (−3,10). Compute the following f(-8)…

A:

Q: Using Secant method, the approximation of the root of the function f(x) = xe*-x - 1 %3D accurate to…

A: The given function is f(x)=xex-x-1 And x0=0.7   &amp;  x1=0.76

Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: (i) Consider the function such that f(x) = 2x if 0SxS1 and f(x) = x-1 if x> 1. Is f continuous over…

A:

Q: 26. Show that the function has removable discontinuity at the origin sin 2x {²7, 2x 1 f(x) = if x =…

A:

Q: Expand the function f(x) = x, 0 < x < 2, in half range sine series. 4 O (A) (#) = - sin()- sin() -…

A:

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: