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Calculus Questions
What is the area inside the larger loop but outside the smaller loop of the curve?...
Find the second degree polynomial of Taylor series for f(x)= 1/(lnx)^3 centered at c=2. Write step...
A 2525-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides...
A salon sells its cologne wholesale for $8.75 per bottle. The variable costs of producing x...
1. Evaluate the following indefinite integrals using integration by parts. Show your work please: a) ∫...
Suppose the rate of change of the temperature of a body is proportional to the difference...
3. Determine the open intervals on which each function is increasing / decreasing and identify all...
Find the volume V of the solid obtained by rotating the region bounded by the given...
17. The velocity function, in feet per second, is given for a particle moving along a...
Your company manufactures two models of speakers, the Ultra Mini and the Big Stack. Demand for...
Let f(x)=ln[x^3(x+5)^5(x^2+4)^6] f '(x)=
A fence must be built to enclose a rectangular area of 140,000 m2. Fencing material costs...
Find the length of the curve x= (3t - t)^3, y = 3(t^2) for 0 ≤...
Why Newton's Method works at x0=-2 in f(x) = x^3-2x+2?
integrar x[(sen(x2+1)cos(x2-1)]dx
Find that value of a such that ∫1a cube root(x)+2/cube root(x) dx=98/27.
The equation y = 2e6x - 5 is a particular solution to which of the following...
Find the equations for the tangent line and the normal line to the curve. x=sen^2(xy) on...
Water is leaking out of an inverted conical tank at a rate of 1100011000 cubic centimeters...
Two people start from the same point. One walks east at 9 mi/h and the other...
Evaluate the surface integral of the vector field ?⃑(?, ?, ?) = 〈?, ?, ?〉 along...
Consider The Power Series: ∞∑n=0 (2x)^n a)Find the radius of convergence b)Find the interval of convergence
Find the first derivative ?′ and the original function ?. ?″(?)=?3−18?, ?′(1)=0, ?(1)=8
Determine the absolute minimum and maximum values of the function f(x, y) = 2x^2 −2xy +y^2...
Use implicit differentiation to find dy/dx given 6sin(2x+3y)=7xy
Consider the function f(x)=ln(x2 +4)[6+6+8=16 marks] Note: f'(x) = 2x divided by (x2 +4) f''(x )...
The annual net income of a company for the period 2007–2011 could be approximated by P(t)...
A small island is 3 miles from the nearest point P on the straight shoreline of...
consider the function f(x) = x/1-x^2 (a) Find the open intervals on which f is increasing...
Let C be the hexagon in 3-space with corners at (−2,0,3), (−1,−5,3), (1,−5,3), (2,0,3), (1, 5,...
Which of the following are critical numbers of the function f(x)=x4−2x2+5 ?
Find the number of solutions of the following DE for various all real values of b>0:...
The marginal cost, in dollars per unit, for a company's portable heater is C'(q) = 48...
What are the dimensions of the lightest open-top right circular cylindrical can that will hold a...
Find the volume of the solid of revolution formed by rotating the area under the graph...
Find the slope of the tangent line to the cuve sqrt(7x+y) + sqrt(3xy) = 11 at...
The temperature on the surface of the sphere x^2+y^2+z^2=9 is given by T(x,y,z)=2x+2y+z, What is the...
Suppose f(5) = 2 and f′(5) = −0.5. Estimate f(6).
At which point does the function f(x) = 96xex3+7x−1 have a horizontal tangent line? (A) (−1.16667,...
Find y' and y'' for x2 + 6xy − 5y2 = 4.
1.) Find the equation of the tangent line to the graph of the function f(x)=5x-4/2x+2 at...
Logarithmic differentiation to differentiate: y = 3x^(3x)
Write the partial fraction decomposition of the following rational expression. (x^2-5x+12)/(x-5)(x-2)(x+1)
Find f. f '''(x) = cos(x), f(0) = 1, f '(0) = 3, f ''(0) = 7 f(x) =...
1) Explain how sequences are used to find the sum of an infinite series 2) Explain...
rewrite the geometric series 1/8+2/80+4/800+8/8000+.....with summation notation and determine if it converges or diverges if the...
7. A rectangular storage container with an open top is to have a volume of 10...
calculate lim (x-0) (e^x-1)/sinx
A company has a plant in Scranton and a plant in Salt Lake City. The firm...
What type of polynomial is the golden state bridge in San Francisco?
Brand Z's annual sales are affected by the sales of related products X and Y as...
Find an equation of the tangent to the curve at the given point by both eliminating...
Find the Laplace transform F(s) = ℒ{ f (t)} of the function f (t) = (7...
Consider the region in the xy-plane bounded by the curves y = 3√x, x = 4...
Find the directions in which the function increases and decreases most rapidly at p0.Then find the...
Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an answer...
1.) Use the second derivative test to find the relative extrema for f(x) = x4 –...
Find the general solution of the following differential equation. Primes denote derivatives with respect to x....
Let the function f be defined as f(x) = x 2 − x + 30, where...
consider the funtion f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and f''(x)=-10x^2-9x+5/(x^2+1)^5/2 a) Find the domain of f. (write...
Vehicle A is headed due west from a fixed point PP at a rate of 4545...
Let D be the region enclosed by the cone z =x2 + y2 between the planes...
The complex has 250 available living spaces. Our monthly profit in dollars is modeled by the...
Consider the function on the interval (0, 2π). f(x) = sin(x)/ 2 + (cos(x))2 (a) Find...
1 C. A reservoir in the shape of a straight circular cone is filled with water....
Jared throws a penny off the top of a building that is 240 feet tall. The...
find the area of y=x^2 -6x +8 y= 2x-7
Use Lagrange Multipliers to find the maximum and minimum values for ?(?, ?) = ?2? given...
The general solution of the system of coupled equations d x d t = 2 x...
Please show all work to the problem. Thanks! The problem is to find the solution to...
Be sure to highlight the step (illustrated below) in your answer sheet, when using the chain,...
1. For each value below, enter the number correct to four decimal places. Suppose an arrow...
Differentiate the function. s(t) = 2t − 4(2t^4 + 2)^3 Find the indicated derivative. dz/dx for...
The velocity function of a particle is given by v(t) = 3t2 – 24t + 36....
Use Taylor Series to estimate the value of ln(3.4) knowing that the value of ln(1)=0 ,Perform...
After a large number of drinks, a person has a blood-alcohol level of 200 mg/dL (milligrams...
Use the Theorem of Pappus to find the volume of the given solid. The solid obtained...
An aquarium that holds 40 cubic meters of water is to be made such that the...
a) Find the equation of the tangent line to f(x) = e –x at the point...
A space curve C is parametrically parametrically defined by x(t)=e^t^(2) −10, y(t)=2t^(3/2) +10, z(t)=−π, t∈[0,+∞). (a)...
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