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Calculus Questions
a rectangular box with an open top and one partition is to be constructed from 288...
Find the linear, quadratic, and cubic approximations for f(x) = the square root of (x+1)
A farmer was told by the municipality to enclose a field by a river to keep...
Find the linear, quadratic and cubic approximations for f(x) = e^x.
Express the integrand as a sum of partial fractions and evaluate the integral. integral 6x-9/x^2-3x-40
1) which of the following is a linear approximation of the function f(x)= sqrt[ 4 ]...
Find the local extrema of the following function. f(x,y) = x3-3xy2+15y2
Find the maximum and minimum values of f(x,y)=81x2+y2f(x,y)=81x2+y2 subject to the constraint 4x2+y2=94x2+y2=9.
Given F(2) = 1, F'(2) = 7, F(4) = 3, F′(4) = 7 and G (4)...
-Let a and b be the vectors a = (1,−2,2) and b = (−3,4,0). (a) Compute...
Find the mass and center of mass of the lamina that occupies the region D and...
Let D be the smaller cap cut from a solid ball of radius 2 units by...
1. The profit (in dollars) form the sale of x lawn movers is P(x)= 60x-0.06x2-350. (A)...
Sketch the region enclosed by the given curves and find its area: a)y=x^2-4 b)y=x+2 1<=x<=4
Briefly describe what an asymptote is and why asymptotes are so important in calculus. Don't forget...
A large tank is filled with 80 gallons of fluid in which 2 pounds of salt...
Find the absolute maximum and minimum values of f on given intervals: (a) f(x) = x^4...
The number (in millions) of employees working in educational services in a particular country was 13.2...
The average home attendance per week at a Class AA baseball park varied according to the...
Let R be the region bounded by y = x2 + 1, y = 0, x...
In regards to the function f(x,y) = xye^y+2x. Find Duf(1,0) in the direction of the vector...
An inferior product with an extensive advertising campaign does well when it is released, but sales...
The table shows the number of days that milk will keep as a function of the...
What is the definite integral of ?
Differential Equations: A 77 kg sprinter jumps over a hurdle that is 0.8 m above the...
Sketch the regions enclosed by the given curves. Decide whether to integrate with respect to x...
find the maximum, minimum and point of inflexion of f(x)= ((x^3)/3) - x^2
For the function y(x) = 3 2 x 2 − 5x + 1: a) Determine the...
two vectors equal⟨1,−3,−2⟩andv=⟨−2,−1,−1⟩determineaplanein space. Without using linear algebra and or row reduction, determine whether the following...
A spherical balloon is being filled with helium at the constant rate of 16πdm3/min. Calculate the...
Set up each problem to be solve using both disk/washer and shell method. Identify which is...
What are the equations of the tangent and normal lines to the following curve: y2+y+x=arctan2(sin3(x)) at...
In a study prepared in 2000, the percentage of households using online banking was projected to...
The demand function for a certain brand of CD is given by p = −0.01x^2 −...
9a. Find a set of parametric equations for a circle with a radius of 3 centered...
The length ℓ, width w, and height h of a box change with time. At a...
Using langragrean, Find the values of x, y and z that minimise (x^4 + y^4 +...
Consider the graph of the function z=2x-3y+c in a plane. In case of c=4, find three...
A study of U.S. colleges and universities resulted in the demand equation q = 20, 000...
Find the total value of the given income stream over the interval 0 ≤ t ≤10...
1- Find the area enclosed by the given curves. Find the area of the region in...
In a 2 sec lab experiment a particle moves in a straight line while its acceleration...
There is gas in the trough and the gas has a density of 2000 ??/?3 ....
Show that there is a solution to the equation e^x=3-2x in the interval(0,1)
6. Let ?(?) be a continuous function defined for all real numbers, with?'(?)=(?−1)2(?−3)3(?−2) and ?''(?) =...
Find the angle, in degrees, between the planes 2x-3y+6z=5 and x-2y+2z=4. Respond the obtuse angle between...
Find the unit tangent vector T and the principal unit normal vector N for the following...
given the following supply and demand functions find the consumer's surplus and producer's surplus. s(x)= 0.09x2...
Find the directional derivative of the given function where (x,y)=(1,1) in the indicated direction Direction <3,4>...
If f(2)=100, what is the value of f(5)?
The base of a solid is the region in the first quadrant bounded by the graph...
Find the minimum and maximum of F(x)=x^3-ax
Use the Chain Rule to find the indicated partial derivatives. P = sqrt(u2 + v2 +...
1. Use a definition of a Taylor polynomial to find the Taylor polynomial T2(x) for f(x)...
Use shell method to find the volume of the solid generated by revolving the region bounded...
Given the function f(x)=−2+x^2, calculate the following values: f(x+1) ; f(x)+f(-4)
The altitude of a triangle is increasing at a rate of 1 cm/min while the area...
1. Evaluate the limit using L'Hospital's rule if necessary lim x→∞ (1+ 12 / x)^x/1 2....
Find the quadratic approximation (Taylor Polynomial) for f(x,y) = 2xe^(2y) near (2,0).
A furniture store sells two styles of a chair, reclining and non-reclining. During the month of...
Suppose that over a certain region of space the electrical potential V is given by the...
if F(x,y)=2xyi+(x^2+2y)j , find the work done by compute fc(F) *dr , where C is an...
A trough is 4 feet long and 11 foot high. The vertical cross-section of the trough...
Find the absolute maximum and minimum values of f on the set D. f(x,y)=2x^3 +y^4 +2,...
Find the curvature of the curve r(t)= < et , t , t2 >.
I am having trouble simplifying this question as most of my examples are different than this....
Find the global maximum and global minimum of f(x, y) = y^2 +xy −x^2 on the...
Find an equation for the line tangent to the curve at the point defined by the...
Let Y = 3x2 + 12 x find Y` ____0____ Find the critical point(s) for Y`...
Find the total flux of F = −xi−yj + (z^2)k through the portion S of the...
Let C ⊂R3 be the parametrized curve X(t) = (√2t, (2/3)t^(3/2), (2/3)t^(3/2) ), t ∈ [0,1]....
Calculate ∬Se^(−z)dS where S is the surface given by x2+y2=4, 0≤z≤7.
A swimming pool is 50 ft wide and 100 ft long and its bottom is an...
Set up a double integral to find the flux of the vector field F = <−x,...
6) Given y = [ e ^ (2x+1) ] / [2 ^ (1 - 3x)], then...
1a) Evaluate the limit as x goes to infinity using l'hopitals rule (x^-1/3)/sin(1/x) 1b) Evaluate the...
Let f(x)=6x^2−2x^4. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates...
Given two planes in space: 2? − ? + 6? = −4 and 5? + 3?...
calculate ∫ sin^2 (wt) dt
2. Where H iis the patient’s height in cm, w is the patient’s weight in kg,...
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