Question

If cos x is replaced by 1 - (x2/2) and |x |<0.5, what estimate can be made of the error? Does 1 - (x2/2) tend to be too large, or too small? Give reasons for your answer.

Expert Solution

Want to see the full answer?

Check out a sample Q&A here
Blurred answer
Students who’ve seen this question also like:
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
Not helpful? See similar books
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
The Trigonometric Functions. 24E
marketing sidebar icon
Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: (3) Estimate the error involved in using the approximation cos x = 1- for |x| < 0.01

A: To estimate the error involved in using the approximation cosx≈1-x22 for x≤0.01 The Taylor series…

Q: The equation f(x) is given as cos x - x2 - x = 0. Considering the initial approximation at %3D Xo=…

A: This question is taken from the numerical methods in which we have to the next approximation value…

Q: The equation xsin x + cos x =1.015 has a positive root a close to zero. Use small-ar approximations…

A: Click to see the answer

Q: Show that 1 − cos x = x2/2 with an error less than 0.003 for |x| &lt; 1/2.

A: Given: 1-cos x =x22;    |error|&lt;0.003Formula:  The…

Q: - cos (4x)= sin (x) cos (x) on the interval [0,27]

A: Click to see the answer

Q: 1-Find the first derivative of the following function f( x) 5 cos (10x) + x' – 2x – 6x+ 10 For x=2…

A: Click to see the answer

Q: 2. Find the root of the function using Fixed-point Iteration. f (x) = x cos (x) - x?

A: Consider the given function as, fx=xcosx-x2

Q: 2- Find the positive root of f(x) = xe"- cos(x) with an error tolerance =0.005% by using the secant…

A: Using a graph, it can be found out whether a function has solutions if the graph cuts the x-axis at…

Q: The nth derivatives of sinªx is ㅎ4"cos(4x +

A: FALSE. SOLUTION IS GIVEN BELOW HANDWRITTEN DOCUMENT. nth derivative of sin^4x

Q: At what points do the local and absolute extreme values of the function (x) = 2 cos x- x^2 occur on…

A: We have to solve given problem:

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given :             cosh(3x2y) = x + ln(exy + 1)   To find :            ∂y∂x

Q: Find the linear approximation of f(x) = cos(x) at x = * and use it to approximate cos(134°). Give…

A: The formula for the linear approximation is: L(x)=f(a)+f'(a)(x-a) Here, given function is…

Q: On the graph of f(x)=sinx and the interval [0,2π), for what value of x does the graph cross the…

A: Plot the graph of sinx given below

Q: Find the linear approximation of f(x)=cos(x) at x=3π/4 and use it to approximate cos(137∘). Give…

A: Click to see the answer

Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

Q: Find the possible values of cosh x that satisfies sinh²x – 3 cosh x + 3 = 0

A: We use the following identity to solve question 1). cosh2x - sinh2x = 1

Q: Use Simpson's rule to calculate x² sin x dx to within 2 x 10-5 of the exact

A: Click to see the answer

Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x &amp; cos-1x

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

A: Click to see the answer

Q: е. Verify that the derivatives of sinh z. f. Solve the value of sinh(2 – iV9) as well as their…

A: Click to see the answer

Q: е. Verify that the derivatives of sinh z. f. Solve the value of sinh(2 – iv9) as well as their…

A: Click to see the answer

Q: е. Verify that the derivatives of sinh z. f. Solve the value of sinh(2 – iv9) as well as their…

A: Click to see the answer

Q: е. Verify that the derivatives of sinh z. f. Solve the value of sinh(2 – iv9) as well as their…

A: Click to see the answer

Q: е. Verify that the derivatives of sinh z. f. Solve the value of sinh(2 – iv9) as well as their…

A: Click to see the answer

Q: е. Verify that the derivatives of sinh z. f. Solve the value of sinh(2 – iv9) as well as their…

A: Click to see the answer

Q: е. Verify that the derivatives of sinh z. f. Solve the value of sinh(2 – iv9) as well as their…

A: Click to see the answer

Q: е. Verify that the derivatives of sinh z. f. Solve the value of sinh(2 – iv9) as well as their…

A: Click to see the answer

Q: 2. Find a reduction formula for sin" x dx. By using this formula evaluate sin® x dx.

A: The objective of the question is determine the integral.

Q: Show that sin(x^2) ≤ sin x for 0 ≤ x ≤ 1. Deduce that sin(x^2) dx ≤√2/2 on the invterval [0, π/4]

A: Click to see the answer

Q: ) Use the simple fixed point iteration method to find a root of th cos x with initial guess x, =4…

A: To find a root of the equation x3=-cosx using the simple fixed point iteration method with initial…

Q: If f (x) = - cos(x), then f (10) (x) is equal to (A) - sin (x) ® -cos(x) © sin(x) D cos(x)

A: Click to see the answer

Q: On the graph of f(x)=tanx and the interval [0,2π), for what value of x does the graph meet the…

A: x 0 π4 3π4 π2 π 5π4 3π2 7π4     tanx 0 1 3 ∞ 0 -1 -∞ -3

Q: 1.) Determine the root of the equation by Fixed Point Iteration (Should converge at three decimal…

A: First we write x=g(x) then find convergent point.

Q: On the graph of f(x)=tanx and the interval [−2π,0), for what value of x does the graph meet the…

A: To Determine: What value of x does the graph meet the x-axis. Given function is :…

Q: In the given question, verify the identity:-   cosh x - sinh x =- e-x

A: We have to verify the following identity: cosh x-sinh x=e-x We know that, sinh x=ex-e-x2cosh…

Q: In the given question, verify the identity:- cosh x - sinh x =- e-x

A: As we know that the hyperbolic function of the inverse trigonometric identity is given by as…

Q: Graph the function defined as follows over a two-period interval. y = -3 tan x

A: To graphy=-3 tanx

Q: EX / Show that cosh x-sinhx=1

A: Click to see the answer

Q: Use a linear approximation of f(x)=cos(x) at x=5π/4 to approximate cos(222∘)

A: Click to see the answer

Q: If g(x) : 8 + cosh(9x) find g'(x) 8+ cosh(0)

A: Answer and explanation is given below

Q: Without evaluating derivatives, which of the following func- tions have the same derivative: f(x) =…

A: Given: fx=sin2x, gx=-cos2x, hx=2sin2x, px=1cosec2x For finding which function have same derivatives,…

Knowledge Booster
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage
  • Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage