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Calculus Questions
Determine the centroid, C(x̅, y̅, z̅), of the solid formed in the first octant bounded by...
Consider the region bounded by y = sin x and y = − sin x from...
Let R in the x,y-plane be in the first quadrant and bounded by y=x+2 and y=x2,...
Given that f(x) = Cax for some positive constants C and a, sketch the graph of...
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
A person took a trip of 224 miles by car in 3.5 hours, from North Carolina...
Set up but do not evaluate. Do not foil or anything like that. Set up the...
An integral equation is an equation that contains an unknown function y(x) and an integral that...
Find the general solution of the given differential equation. State an interval on which the general...
f(x)=3tan(sqrt(x)). find f'(28) AND f(x)=ln(6+cox(9x)). find f'(8)
Calculate the average rate of change of the given function f over the intervals [a, a...
Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x,...
The sun is shining and a spherical snowball of volume 400 ft3 is melting at a...
Suppose you need to know an equation of the tangent plane to a surface S at...
In a murder investigation, the temperature of the corpse was 33°C at 1:30pm and 18°C 5...
Integrate (x^3)*sqrt(x^2 +4) dx, using trigonometric substitution.
Elasticity of Demand for Ink-Jet Cartridges The demand function for a certain make of ink-jet cartridge...
or the following demand equation compute the elasticity of demand and determine whether the demand is...
City cabs charges a $2.5 pickup fee and $1.5 per mile traveled. (a) Express the cab...
For the following demand equation compute the elasticity of demand and determine whether the demand is...
Find the family of curves orthogonal to: y3 = k(x − 4)2.
Williams Commuter Air Service realizes a monthly revenue represented by the following function, where R(x) is...
Which of the following ODEs (there may be more than one) have steady-state solutions: y''+2y'+3y=13cos(14t) y''−2y'+3y=13cos(14t)...
B) Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(7,0,0),(0,4,0),(0,0,6)
Are the vectors a = i + j − k, b = i − j +...
The hyperbolic cosine function, cosh x = (1/2) (e^x + e^-x). Find the Taylor series representation...
f is an integral from 0 to x^2 x*sin(pi*x) for x > 0 calculate f(35)
1. Determine the centroid of the area bounded by the y − axis, the x −...
To test an individual's use of a certain mineral, a researcher injects a small amount of...
The bottom end A of a 20-foot ladder is resting on the ground, while its top...
Use Taylor’s Inequality to determine the number of terms of the Maclaurin series for ex that...
find the area of one leaf of the polar curve r = 2sin(8theta)
Please answer the following problems using COMPLETE and GRAMMATICALLY CORRECT sentences. Please provide all supporting work...
Use the definition to find an expression for the area under the graph of f as...
Find the local linear approximation of f(x,y) = x + tan(xy - 6) at the point...
A rectangle has two of its vertices on the X axis and the other two above...
Verify that the function f(x)=(1/3)x3+x2−3x attains an absolute maximum and absolute minimum on [0,2]. Find the...
Let F(x,y,z) = yzi + xzj + (xy+2z)k show that vector field F is conservative by...
Find a unit normal vector for the following function at the point P(−1,3,−10): f(x,y)=ln(−x/(−3y−z))
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x)...
Draw a diagram of the region of integration. Then reverse the order of integration and evaluate...
Find the degree 3 Taylor polynomial T3 (x) centered at a = 4 of the function...
Find the indefinite integral of (x arctanx)/(1+x^2)^2
exact differential equation, (2xy+x)dx+(x^2+y)dy=0
Convert the following summations to summation notation, then use Therom 5.1 to simplify and find the...
Evaluate the limit, using L'Hôpital's Rule if necessary. lim x→∞ X^3/5e^x/3
Find an equation of the plane. The plane through the point (1, 0, 3) and perpendicular...
The demand for tickets to an amusement park is given by p=70−0.04q, where p is the...
Determining Volumes by the Disk-Washer Method 1. Find the volume of the solid formed by revolving...
A dinghy is pulled toward a dock by a rope from the bow through a ring...
Identify the curve by finding a Cartesian equation for the curve r = 3 tan ...
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...
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