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Calculus Questions
U.S. National Debt The U.S. national debt stood at $10.025 trillion in 2008 (t = 0)...
The path of a particle on a two-dimensional surface is defined by ln? (x/y)? = sin-1(x...
What is the area of the region common to two regions bounded by circle r=3, and...
A) Use the arc length formula to find the length of the curve y = 2x...
Consider the graph of y=f(x)=1−x2 and a typical point P on the graph in the first quadrant....
A) let f(x)=4x^(4x) find f'(3) f'(3)= B) let y=x^(logbase6(x)) dy/dx=??? must express answer ini terms of...
a) Find the point(s) on the ellipse 4x^2 +y^2 =4 that are farthest away from the...
Compute the following limit using l'Hospital's rule if appropriate. limx→∞ x5e-x^2 (reads x to the 5th...
Solve the first-order linear differential equation: y ′ + sin ( x ) y =...
solve (x^2+2y^2)dx/dy = xy
given the planes P1 and P2 determine whether the planes intersect or are parallel. if they...
use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a...
Find the equation for (A) the tangent plane and (B) the normal line at the point...
A mug of beer chilled to 30 degrees, if left in a 72-degree room, will warm...
Set up, but do not evaluate or simplify, the definite integral(s) which could be used to...
Consider a wire of length L which is to be cut into two separate pieces. The...
Consider the curve c(t) = (t – 2sin(t), 1 – 2cos(t)). (a) Find an equation for...
At time t = 0, a ship leaves point P and heads north at 4 km/h....
For Problems 33–36, find the general solution to the given differential equation and the maximum interval...
t(s) 0 12 24 36 48 60 v(ft/s) 23 27 30 20 33 20 Speedometer readings...
A real estate office manages an apartment complex with 40 units. When the rent is $660...
a circular cone shaped tank that is 10 feet high, is filled to about 2 feet...
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫ F...
1. Use the shell method to set up and evaluate the integral that gives the volume...
Find the area of the region that is enclosed between y= 4sin(x) and y= 3cos(x) from...
Find an equation of the plane. The plane that passes through the line of intersection of...
Use the model for projectile motion, assuming there is no air resistance and g=32 feet per...
Let F(x, y, z) = (3x2 ln(6y2 + 2) + 8z3) i + ( 12yx3 6y2...
Write the equations in cylindrical coordinates. (a) 8x2 − 7x + 8y2 + z2 = 1 (b) z...
Find the work done by the following force field F(x, y) = 7(y + 2)5 i ...
Which of the following vector fields are conservative? (i) F(x, y) = (7x6y6 + 3) i ...
Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the point....
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
Determine over which intervals the following functions are increasing, decreasing, concave up, and concave down. a.)...
Tangent Line Approximation, Given this ellipse 5x² - 6xy +5y^2 = 16 differentiate implicitly to get...
A particular study showed that a group of people learned new language characters according to L(t)...
Let f(x, y) =sqrt(1−xy) and consider the surface S defined by z=f(x, y). find a vector...
Use Euler’s formula to solve 2sin 3x − 2cos 3x = √6 Write z = 4i...
The price/unit from the sale of X units in a monopoly market is given by: ...
i) lim x→3 (4x − 12)/x2-5x+6 ii)lim x→+∞ (e2x-1-x)/x2 iii)limx→0 (sinh(x2))/ cosh x-1 iv) limx→0 sin2x/sin7x
A snowball is melting so that its surface area is decreasing at a rate of 2...
Determine the convergence/divergence of the following series using the integral test: a.) ∑= (1)/n(In(n))^2 (Upper limit...
Use the shell method to find the volume of the solid generated by revolving the region...
Find the general solution of the differential equation y′′ − 2y′ − 3y = ae3t, where...
1. Suppose(x0,y0) is the closest point on the line that is the graph of y=5x+7 and...
Find the Fourier series for f(x)= p-x on -p<x<p
You want to estimate the area underneath the graph of a positive function by using four...
y´´+4y´+6y=0, y(0)=1, y´(0)= -4 Use Laplace Tranfrom, as quick as possible please.
Find dy/dx, given sin(x^2+y^2)=4xy PLEASE , no Hospital Rule and please check for comments later on...
Question No.1: A car was purchased for 5400 RO and is sold for 4300 RO. What...
If a1= 3 and a=6 1/8 in an {an} geometric array, find the general term of...
1) Create a function for which finding the first derivative would involve a minimum of two...
Consider the following limit. lim (x^2 + 4) (x--> 5) 1. Find the limit L. 2....
Consider the boundary value problem below (assume λ > 0): y ′′ + λy = 0...
Let a = 2i -3k; b= i+j-k 1) Find a x b. 2) Find the vector...
box with rectangular base to be constucted material cost $4 /in^2 for the side & $5/in^2...
A sphere with radius 1 m has temperature 11°C. It lies inside a concentric sphere with...
The given point is on the curve.Find the that are (a) tangent and (b) normal to...
Integrate ∫ tan 3 ( 2 ? ) sec3 ( 2 ? ) ??
Find the area of the indicated region. We suggest you graph the curves to check whether...
Consider the function f(x)=arctan((x+5)/(x+4)) What is the slope of the tangent line at the inflection point?...
Consider the initial value problem y''−y'+14y= 0, y(0) = 2, y'(0) =b, determine the value of...
The marginal revenue of the xth box of flash cards sold is 400e−0.001x dollars per box....
An object is moving in the plane according to the parametric equations x(t)=8sin(π t) y(t)=4cos(π t)...
A man on the sixth floor of a building sees a bucket (dropped by a window...
1.) P(2, 4) lies on the graph of y=x4-2x-4 Q is the point (x, x4-2x-4) Write...
Use Stokes' Theorem to evaluate ∫ C F · dr where F = (x + 8z) ...
A piece of wire of length 70 is cut into two pieces. One piece is bent...
Use the divergence theorem to find the outward flux ∫ ∫ S F · n dS ...
Estimate the minimum number of subintervals needed to approximate the integral integral subscript 0 superscript 4...
Find the point on the line −4x+7y+4=0 which is closest to the point (4,−4). Answer is...
f(x)=x^4-2x^2+5 on interval -2<(or equal to) x < (or equal) 1 FIND MAX AND MIN
The line ?=3?+970y=3x+970 is tangent to the graph of ?=2?3−3?2−249?−2 at the point...
find the directional derivative of f(x, y, z) = xy arctan (z) at the point (1,...
Find the equation of the tangent plane to the surface given by z = ln (2tan...
1) (a) Determine if the following statements are true or false. If true give a reason...
shows that the 3x-6y + 2z = 5 plane is parallel to the line x =...
Solve the differential equation y^' − xy = e^x y(0) = 2
Consider the function ?(?)=2?^3+12?^2−72?+2, −6≤?≤3 a) Find the absolute minimum value b) Find the absolute maximum...
Find the length of the polar curve r = e^-theta, o lesser or equal to theta...
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