Question

The estimate sqrt(1 + x) = 1 + (x/2) is used when x is small. Estimate the error when | x|< 0.01.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

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.
Tagged in
Math
Calculus

Other

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: Given the cost and price functions C(q)-100q+49,000 and p(q)=-2.6q+870, if the company sets the pric...

A: Given

Q: Find the centroid of the region in the plane enclosed by the curves y = +-(1 - x2)^(-1/2) and the li...

A: Click to see the answer

Q: Use Taylor’s formula with a = 0 and n = 3 to find the standard cubic approximation of ƒ(x) = 1/(1 - ...

A: The given function is,

Q: Hi, I have some homework for my calculus class that I can't figure out. I worked it out and got it w...

A: Given,

Q: Show that ϕ(t) = e2t is a solution of y′ − 2y = 0 and that y = cϕ(t) is also a solution of this equa...

A: Proof: part (a). Given

Q: Solve the following initial value problem for u as a function of t: du/dt+k/ m u = 0 (k and m positi...

A: Plug du/dt = u' to make it first-order linear equation.

Q: A region in the first quadrant is bounded above by the curve y = cosh x, below by the curve y = sinh...

A: A region in the first quadrant is bounded above by the curve y = cosh x, below by the curve y = sinh...

Q: A colony of bacteria is grown under ideal conditions in a laboratory so that the population increase...

A: Given:At the end of 3 hours there are 10,000 bacteria.At the end of 5 hours there are 40,000 bacteri...

Q: Consider the region bounded by the graphs of y = sin-1 x, y = 0, and x = 1/2. a. Find the area of th...

A: The given curves are,

Q: what is the left and right endpoint Riemann sum for f(x)= (x^2)/11 on the interval [2,6]?

A: Given:

Q: solve the differential equation. 1.e-x dy + (e-xy - 4x) dx = 0 2. (x + 3y2) dy + y dx = 0 (Hint: d(x...

A: Consider the provided differential equation,

Q: Solve the homogeneous equations (x2 + y2) dx + xy dy = 0

A: Click to see the answer

Q: xy′ = (1 − y2)1/2

A: Put y'= dy/dx Then separate the variables. 

Q: Find the lengths of the curves in Exercises 55 and 56. 55. y = (x2/8) - ln x, 4 &lt;=x&lt;=8 56. x =...

A: Given:

Q: A ball with mass 0.15 kg is thrown upward with initial velocity 20 m/s from the roof of a building 3...

A: To determine,Part (a) The maximum height attained by the ball.Part (b) The time when the ball hits t...

Q: The region enclosed by the curve y = sech x, the x-axis, and the lines x = +- ln sqrt(3) is revolved...

A: Given:

Q: A tank initially contains 120 L of pure water. A mixture containing a concentration of γ g/L of salt...

A: A tank initially contains 120 L of pure water. A mixture containing a concentration of γ g/L of salt...

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0  What are the critical numbers of the function?

A: Given function is

Q: In Exercises 31–32, find the volumes of the solids generated by revolving the regions about the give...

A: (a)Given information:

Q: What values of p have the following property: The area of the region between the curve y = x^-p, 1&l...

A: Given information:

Q: A solid is generated by revolving about the x-axis the region bound-ed by the graph of the positive ...

A: Click to see the answer

Q: The Cinema Center consists of four theaters: Cinemas I, II, III, and IV. The admission price for one...

A: Click to see the answer

Q: Suppose that the position of a body moving along a coordinate line at time t is a. s = a cos kt + b ...

A: Part (a):Part (a):Given,Given,

Q: consider the equation f(x) = 2x2 - x Find the net change between x = 3 and x = 6

A: Given equation:

Q: y′ + y2 sin x = 0

A: The given differential equation is

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 What are the vertical asymptotes?

A: Given function is,

Q: The region in the first quadrant that is bounded above by the curve y = 1/x^(1/4), on the left by th...

A: Graph the situation using graphing calculatorWe have to rotate the shaded region.

Q: Solve the initial value problem y′=2y2+xy2,y(0)=1

A: Given an initial value problem,y′ = 2y2+xy2, y(0) = 1

Q: The temperature at which water starts to boil​ (its boiling​ point) is linearly related to the altit...

A: Let 1000x ( x times 1000)  feet above sea level you need to be in order to have a boiling point of 1...

Q: find the volume  The solid lies between planes perpendicular to the x-axis at x = 0 and x = 4. The c...

A: Given,

Q: x dx+ye−xdy=0,y(0)=1

A: Click to see the answer

Q: A painting attributed to Vermeer (1632–1675), which should contain no more than 96.2% of its origina...

A: To determine the time (in years) of forgery, A painting attributed to Vermeer (1632-1675), which sho...

Q: Use the shell method to find the volumes of the solids generated by revolving the regions bounded by...

A: Since we only answer the first question, we’ll answer the first. Please resubmit the question and sp...

Q: find the Taylor series at x = 0 of the functions in Exercises 1–2. 1.ln(3+6x) 2. 5sin ( -x)

A: Consider the given question,(1)The Taylor series at x = 0 is given by,

Q: Find the surface area of the cone frustum generated by revolv-ing the line segment y = (x/2) + (1/2)...

A: Given:

Q: What are the derivatives of the six basic hyperbolic functions? What are the corresponding integral ...

A: The derivatives of the six basic hyperbolic functions are as follows.

Q: Solve the inequality. Write your answer in interval notation. -7x &gt; -2x2 + 15

A: Given:

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 Where is the function increasing and decreasing in inte...

A: Click to see the answer

Q: (2x? + 3x + 1) dx 3 (a) Find the Riemann sum for this integral using right endpoints and n = 3. (b) ...

A: (a) Obtain the Riemann sum for the given integral using right endpoints and n = 3 as follows.

Q: Find the area of the parallelogram with vertices K(3, 2, 1), L(3, 5, 3), M(5, 10, 3), and N(5, 7, 1)...

A: To find the area of the given parallelogram, use the vector method which is described as.We know tha...

Q: y′ = t2 + y2

A: Click to see the answer

Q: The concentration of an antihista-mine in the bloodstream of a healthy adult is modeled by C = 12.5 ...

A: 6 hour period means from t=0 to t=6That is from start of the medication  to 6 hours after medication...

Q: What integrals lead naturally to inverse hyperbolic functions?

A: Assume

Q: The region between the curve y = 1/x2 and the x-axis from x = 1/2 to x = 2 is revolved about the y-a...

A: Graph the given situation, shaded region is being rotated about y axis

Q: How does ƒ(x) = logx (2) compare with g(x) = log2 (x)? Here is one way to find out. a. Use the equat...

A: We need to plot the two logarithmic functions :