Consider the function. |r + 7|– |r – 7| f(x) = Estimate the following by evaluating fat x-values near 0. (Round your answer to four decimal places.) |x+ 7|– |r – 7| lim Enter a number. Sketch the graph of f.

Q: The region bounded by the curves y = +-4/sqrt(x) and the lines x = 1 and x = 4 is revolved about the...

A:

Q: Find the difference quotient and simplify. f(x)=x2-2x+1,  (f(2+h)-f(2))/h    h cannot = 0

A: Find f(2+h) by plugging x=2+h in f(x)

Q: An aluminum beam was brought from the outside cold into a machine shop where the tem-perature was he...

A:

Q: Use the integral table and a calculator to find to two decimal places the area of the surface genera...

A: Consider the given equation of the curve y = x2,  -1 ≤ x ≤ 1.The surface area of the surface obtaine...

Q: Find the moment about the x-axis of a wire of constant density that lies along the curve y = 2x from...

A: Moment about x-axis is given by the formula.

Q: The life expectancy in years of a component in a microcomputer is exponentially dis-tributed, and 1/...

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Q: How to solve the ordinary differential equation using separation of variables?

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Q: y′+(tan t)y=sin t,y(π)=0

A: Determine an interval in which the solution of the given initial value problem is certain to exist a...

Q: 1f you average 30 mi/h on a 150-mi trip and then return over the same 150 mi at the rate of 50 mi/h,...

A: Given:The average 30 mi/h on a 150-mi trip and then return over the same 150 mi at the rate of 50 mi...

Q: Suppose that a certain population satisfies the initial value problem dy/dt=r(t)y−k,y(0)=y0,dy/dt=r...

A: Calculation:

Q: How does the method of substitution work for definite integrals? Give examples.

A: To elaborate the use of substitution for computing the integrals with example.

Q: Assume that a spring does not follow Hooke’s Law. Instead, the force required to stretch the spring ...

A:

Q: y′ = − y(3 − ty)

A: Given that 

Q: How do you locate the center of mass of a thin plate bounded by two curves y = ƒ(x) and y = g(x) ove...

A: Given:How do you locate the center of mass of a thin plate bounded by two curves y = ƒ(x) and y = g(...

Q: y′ = cos2(x) cos2(2y)

A:

Q: A certain college graduate borrows $8000 to buy a car. The lender charges interest at an annual rate...

A: A certain college graduate borrows $8000 to buy a car. The lender charges interest at an annual rate...

Q: What does it mean when a function does not have any critical numbers. Please explain ALL possibiliti...

A: Critical numbers for any function are defined as the real number x in the domain of the function whe...

Q: evaluate the integral

A: Evaluate the integral by substitution method.

Q: Find the area enclosed by the ellipse x2/ a2 + y2 /b2 = 1

A: Given,

Q: Solve the initial value problems    dy/dx=(x2+1)/x2 , y(1) = -1

A: The given differential equation  is

Q: find the center of mass of a thin plate of constant density d covering the given region. 1. The regi...

A: Given information:

Q: 2y′ + y = 3t2

A:

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: Consider the following two equations. уд Find the values of x for which f(x) = g(x). a.

A: From the given graph of f and g

Q: Sketch the region enclosed by the given curves. x = 9y2, x = 4 + 5y2 У y 1.0- 0.5 6. -0.5 o-1.0- -0....

A: Given curves are

Q: Find the length of the curve y = ln (1 - x2), 0<=x<=1/2

A: Given:

Q: Does ƒ(x) = x3 + 2x + tan x have any local maximum or mini-mum values? Give reasons for your answer.

A: Consider the given function.

Q: In Exercises 47–50, find the volume of the solid generated by revolv-ing each region about the y-axi...

A: The region enclosed by the triangle with vertices (1, 0), (2, 1), and (1, 1)

Q: What is a center of mass? a centroid?

A: To define centre of mass and centroid of an object.

Q: Suppose the amount of oil pumped from one of the canyon wells in Whittier, California, decreases at ...

A: To determine the time (in years), the output of well fall to 1/5 of its present value.

Q: y′=(3x2−ex)/(2y−5),y(0)

A: Given,

Q: The region between the curve y = 1/(2sqrt(x)) and the x-axis from x = 1/4 to x = 4 is revolved about...

A: (a) The given curve is

Q: Evaluate (if possible) the sine, cosine, and tangent at the real number t. (If an answer is undefine...

A: Given:

Q: A particle moves on a coordi-nate line with acceleration a = d2s/dt2 = 15sqrt(t) - (3/sqrt(t)), subj...

A: Given:

Q: Does the graph of y = sqrt(x) - ln x, x> 0, have an inflection point? Try to answer the question ...

A: To determine if the function has an inflection point.Part (a) By GraphingPart (b) By Calculus

Q: The temperature of an ingot of silver is 60°C above room temperature right now. Twenty minutes ago, ...

A: Given,The temperature of an ingot of silver is 60°C above room temperature right now and it was 70°C...

Q: Find the volumes of the solids    The solid lies between planes perpendicular to the x-axis at x = 0...

A: Given,

Q: y′=2x/(1+2y),y(2)=0

A:

Q: Find the length of the graph of y = (1/2) cosh 2x from x = 0 to x = ln sqrt(5).

A:

Q: Square root of p minus square root of p-2 over square root of p

A: Given:Square root of p minus square root of p-2 over square root of p

Q: For what value or values of the constant k will the curve y = x3 + kx2 + 3x - 4 have exactly one hor...

A: To find: -

Q: sin(2x) dx+cos(3y) dy=0,y(π/2)=π/3

A: Given thatSin(2x)dx+cos(3y)dy = 0          …(1)

Q: Express as a single logarithm and if possible simplify

A:

Q: What is the formula for integration by parts? Where does it come from? Why might you want to use it?

A: To explain integration by parts with derivation and use.

Q: If an integrand is a product of the form sin^n x cos^m x, where m and n are nonnegative integers, ho...

A: There can be 4 cases according to that we can consider the values of n and m. Case 1: When m is odd....

Q: Find the total area of the region between the curves y = sin x and y = cos x for 0 <=x<= 3pai/...

A:

Q: Find the area of the region between the curve y = 3 - x2 and the line y = -1 by integrating with res...

A: First of all, find the intersecting points for both the curve.Put y = -1 in first equation and solve...

Q: Find the area of the “triangular” region in the first quadrant that is bounded above by the curve y ...

A:

Q: The charcoal from a tree killed in the volcanic eruption that formed Crater Lake in Oregon contained...

A: The half-life of carbon-14 is 5700 years. The decay constant, k is defined to be