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Provide an example of a function, y = f(x), that is defifined on [5,8], f(5) <...
(Optimization) A rectangular field is to be fenced off along a river where no fence is...
Solve the following differential equations with initial conditions: xy'-y=3xy1/2
f(x) = 1/x from a = 1 to b = 3. (a) Approximate the area under the curve from...
A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type...
Given: v(t) = 6t - 6, on . The velocity function (in meters per second) is given...
Sketch the graph g(x) = | x^2 - 1| - | x^2 - 4 | Write...
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
Express the function f(x) = (x + 10) / (2x^2 − 17x − 9) as the...
The number of women graduating from 4-yr colleges in a particular country grew from 19301930, when...
If f(4) = 5 and f '(x) ≥ 3 for 4 ≤ x ≤ 9, how...
Let R be the region bounded by y = ln(x), the x-axis, and the line x...
Do we know whether or not the following IVP has a unique solution? What theorem tells...
Find the open interval(s) on which the function is increasing and decreasing. Identify the function's local...
find the volume of the solid obtained by rotating the region bounded by the given curves...
Find the area enclosed by ? = ln ? , ? = 2 − ln ?...
1 point) Suppose g is a function which has continuous derivatives, and that g(6)=−1,g′(6)=−3, g′′(6)=3, g′′′(6)=−3...
(2) a) [12 pts] Find the absolute extreme values of the function on the given interval...
solve the laplace transform y''+4y'=8, y(0)=0, y'(0)=0
Given that a function F is differentiable. a f(a) f1(a) 0 0 2 1 2 4...
x2 + (z-1)2 =1 ; y=1 ; y+z=4 Calculate the volume of the closed body...
A zookeeper is designing a rectangular pen for a lion. The area contained in this pen...
For the following nonhomogeneous system of ODEs y' = [TABLE 1 MATRIX] y + [TABLE 2...
Create an example of a plane parallel to the given plane 6x + 3y + 4z...
Find the absolute maximum value and the absolute minimum value of the function f(x,y)=(1+x2)(1−y2) on the...
(10 marks) A rectangular field is to have 100 m2 in area. It is enclosed by...
f(x)=3x^4-7x^2+2x+1 Find the tangent line at x=2
Set up an integral that gives an average value x³ sin x interval [-2, 1].
A deer accelerates at a constant rate from 0mph to 23 mph in 20 seconds. How...
A vitamin water maker finds that the revenue, in dollars, from the sale of x bottles...
f(x)=sinx-sqrt3cosx on(0,2pi) find the intervals of increasing, decreasing , local maximum and minimum
(a) State the integral mean value theorem (b) Find the average value of f(x)=|x| over [-1,4]...
For the function, find the point(s) on the graph at which the tangent line is horizontal....
A total of 200,000 fans spent their money at the NASCAR racing series at Phoenix International...
A horse is running and the distance from the start is given by the function m(t)=25-(t-5)^2...
The function f(x) = x^3+ax^2+bx+7 has a relative extrema at x = 1 and x =...
Suppose that f(2) = −4, g(2) = 2, f '(2) = −5, and g'(2) = 1....
Determine the length of the curve r(t) = 4i + 2t^2 j + 1/3t^3 k from...
Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to...
Determine the equation of the line of intersection of the two planes 5x-2y-2z=1 and 4x+z=6.
Approximate the area under f(x) = (x – 2, above the x-axis, on [2,4] with n...
given a(t) = 30t - 14, v(1) = 2 and s(1) = 3, find v(t) and...
Solve each of the following equations. Implicit answers are acceptable. a.) y'-y= cos(x) with no initial...
Find a particular solution to the given linear system of differential equations: dx1/dt = 4x1 +...
Sketch the graph of a function f(x) that satisfies all of the conditions listed below. Be...
-2 = (-5)^t
The rectangles in the graph below illustrate a left endpoint approximation for the area under ?(?)=?^2/12...
Let f(x)=12x2. (a) If we wish to find the point Q=(x0,y0) on the graph of f(x)...
Use the Midpoint Rule with the given value of n to approximate the integral. Round the...
Find the area completely enclosed by the graphs of f(x) = x^2 - 1 and g(x)...
1. Evaluate ∫tan^2 xsec^4 xdx 2. Evaluate the indefinite integral ∫sin^6 tcos^3 tdt=
Find the equation of the tangent line to the function f(x) = ln(7x) at x=4. (Use...
Estimate ΔfΔf using the Linear Approximation and use a calculator to compute both the error and...
Find the flux of F across S, S F · N dS where N is the...
In 1990 (t = 0), the world use of natural gas was 73874 billion cubic feet,...
use logarithmic differentiation 1. y = (sin(2x))^x 2. y =(3^x)/(1 + 3^x) 3. y= (x+1)^(tan(x))
Find the instantaneous rate of change of the function f(x)=7x^3+7 at x=5. Show your work.
What is the equation of the tangent plane level to 2x2+3y2-4z2=1 at point (1,1,1)?
(Optimization Problem) You're building a fence in a rectangular area for a garden outside of your...
Given that the acceleration vector is a(t)=〈−1cos(t),−1sin(t),−2t〉 the initial velocity is v(0)=<1,0,1> and the initial position...
if y' is equal to (2x-4)^2(x+1)^3, find y'' and draw the graph of y.
Find the absolute extrema of the given function in the given interval f(x) = 4x3+3x2-18x+3 ,...
Estimate the area of the region bounded between the curve f(x) = 1 x+1 and the...
A sheet of paper 64 cm-by-68 cm is made into an open box (i.e. there's no...
Find a set of parametric equations of the line with the given characteristics. (Enter your answers...
so i have a function with f(1) = f'(1) = f''(1) = f'''(1) ..... f^9 (1)...
h(x)=sin[3x+(x^2 +1)^4] what is h'(0)
6. Let series {an} = 1/(n2 + 1) and series {bn} = 1/n2. Use Limit Comparison...
Write down a power series with interval of convergence (0, 4). Write down a power series...
Evaluate the double integral ∬Ry2x2+y2dA, where R is the region that lies between the circles x2+y2=9...
A baseball diamond has sides that are 90 feet long. A player 60 feet from third...
A forest fire covers 1200 acres at time t=0. The fire is growing at a rate...
Find the maximum running speed of an animal that weighs 11 g and grows at a...
Find an explicit formula for f −1 and use it to graph f −1, f, and...
Suppose f(x) is a function and that c is a critical number for f(x) at...
Determine if the series converges conditionally, converges absolutely, or diverges. /sum(n=1 to infinity) ((-1)^n(2n^2))/(n^2+4) /sum(n=1 to...
Approximate the area under f(x) = sqrt(16-x2) from 0 to 4 using four rectangles with left...
the total cost required to produce x units of electrical tape and Y units of packing...
11) Let p(x) = (4x^2-9)/(4x^2-25) (a) What is the domain of the function p(x)? (b) Find...
Please find the dimensions of the largest cylinder that can be inscribed in a sphere with...
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