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Calculus Questions
Find the locations of the maximum and minimum values for f(x)=6x+9y+1 subject to the constraint x2+y2−4=0...
If f(x,y)=(5∗x3+4∗y3+4∗x∗y+1) find the critical point for f(x,y) x=____ y=____ Is this critical point a local...
a(t) = 2e^ −t + 4 cos(2t) − sin(2t). Find the initial acceleration at t =...
volume of solid y =x ,y = x^(1/2) rotating around y = 1
Find the horizontal and vertical asymptotes of the curve. y = x2 + 1 7x2 −...
What is the local maximum and minimum of x4-4x3
1. To test the series ∞∑k=1 1/5√k^3 for convergence, you can use the P-test. (You could...
Find the area of the region enclosed by one leaf of the rose curve ? =...
Use L'Hopitals Rule to evaluate the following limit. lim x-> 0 ( sin(8x) - 8x cos(8x)...
Evaluate the given integral by making an appropriate change of variables, where R is the trapezoidal...
A company wants to design an open top cylindrical bin with volume of 250 cm3. What...
Sketch the region bounded by the given lines ? = 1 − ?, ? = 2...
Equation of a plane containing A= (1,2,-1), B= (1,0,2) and C= (0,2,3)
Find the maximum rate of change and the direction in which it occurs, to f(xy)=ln(x^2+y^2), at...
find the solution of these nonhomogeneous differential equations by using the method of undetermined coefficients y"-...
Find r(t) for the given conditions. r''(t) = −7 cos(t)j − 3 sin(t)k, r'(0) = 3k, r(0) =...
17-foot ladder leans against a wall. The base of the ladder is 11 feet away from...
Consider the following vector function. r(t) = (3sqrt(2)t, e3t, e−3t ) Find the Curvature.
How do you use Gaussian Elimination to work this one out? Solve a system of linear...
Find the relative minimum value of f(x,y)=4x2 +4y2 -2xy, subject to the constraint x+y=4. The value...
A produce and distributor of gift cards produces xx boxes of cards per day at an...
integrate: x^7 sqrt( 64 + x^2)
Use the Divergence Theorem to calculate the surface integral S F · dS; that is, calculate...
At time t = 0 a bacterial culture weighs 1 gram. Two hours later, the culture weighs...
4. Given the function y = f(x) = 2x^3 + 3x^2 – 12x + 2 a....
Q1) (a) What is the distance of a point (x,y) to the line −2x+4y=−16? The solution...
Find parametric equations of the line that passes through (1, 2, 3) and is parallel to...
Calculate the double integral. R 9x sin(x + y) dA, R = (0, pi/6) x (0,pi/3)
Related Rates: Iwhn the theory of relativity, an object that is travelling at an appreciable fraction...
] Evaluate the surface integral SF∙dS for the vector field Fx,y,z=xi+yj+zk , where S is the...
Find the total area between the graph of f(x)=x^2-7 and the x-axis from x=0 to x=7.
What is the volume of a tetrahedron which has a vertices of A (1,2,3), B (2,4,6),...
You want to build a 1100 square foot rectangular infinity pool. Three of the sides will...
State, with explanation, whether the following statements are True or False: a) It is possible for...
An application of the differential: estimation of small changes The power P consumed in a resistor...
2. Discuss the continuity of the following function (responses without reasons will receive no credit): y...
Consider the function f(x, y) = xy and the domain D = {(x, y) | x^2...
Let u = (−3, 2, 1, 0), v = (4, 7, −3, 2), w = (5,...
The yield V (in pounds per acre) for an orchard at age t (in years) is...
An airplane flies at an altitude of y = 4 miles toward a point directly over...
A box is to be created using 28 ft2 of material. If the box has a...
a walker and a cyclist leave a highway intersection at the same time in perpendicular directions....
Problem 7 Find a power series representation for the function and determine the interval of convergence....
Find the normal component of acceleration for r(t)=t2i+t2j+t3k .
Evaluate the integral. 7 t^3i+t(t-6)^1/2j+tsin(pit)k dt 6
solve the initial value problem y' y" - t = 0 y(1) = 2 y'(1) =1
find all the second partial derivatives of f(x,y)= x^2y^2+3sinxtany
A ball is launched straight up in the air from a height of 66 feet. Its...
In 2003, there were 15,600 students at college A, with a projected enrollment increase of 1000...
1. Let ?(?)=8(sin(?))? find f′(2). 2. Let ?(?)=3?sin−1(?) find f′(x) and f'(0.6).
In a certain culture where the rate of growth is proportional to the number present, the...
Figure out the point of intersection of the three planes using the Gauss-Jordan elimination method: 2x...
Using the method of Lagrange Multipliers, find the point on the plane x+y−z=1 that is closest...
1- Differentiate the function g(x) = 7/8x^2 - 7 x + 14 g'(x) = 2- Differentiate...
Determine the volume of the tetrahedron cut from the first octant by the plane 6x +...
1. What is a relative min extrema (x,y) for f(x) in f(x) = 2x3+3x2-12x+5 ? 2....
Given the function M(t) = 2t^3 – 3t^2 – 36t, find the critical values and determine,...
A company makes two types of magazine racks, metal and plastic. The metal magazine racks sell...
Find the volume V obtained by rotating the region bounded by the given curves about the...
1. You've had birthday and forgot to bring breakfast with you at work, so your colleagues...
Find the critical point of the function f(x,y)=x2+y2+xy+12x c=________ Use the Second Derivative Test to determine...
Find the positive value of x that satisfies x=1.3cos(x). Give the answer to six places of...
USING DIFFERENTIAL EQUATIONS To supply an isolated person on an island, they throw a bag of...
1. a) Get the arc length of the curve. r(t)= (cos(t) + tsin(t), sin(t) - tcos(t),...
1) If 67+3?(?)+4?^2(?(?))^3=0 and ?(−4)=−1, find ?′(−4). f'(-4)= 2) Find an equation of the tangent...
1. Find the derivative of f(x)= √4-sin(x)/3-cos(x) 2. Find the derivative of 1/(x^2-sec(8x^2-8))^2
According to the National Health Survey, the heights of adult males in the United States are...
Find a co-terminal angle between 0 degrees and 360 degrees for the angle given: 1525 degrees
2.the graph of x^2 -xy+y^2=6 is a tilted ellipse. Find the coordinated on which the tangent...
For a limited time interval, the current through a 9.71 microhenries (or, equivalently, 9.71×10^-6 henries) inductor...
A particle moves according to a law of motion s = f(t), t ≥ 0, where...
Find the general solution for the given differential equation x2y′′−5xy′+13y=2x3x2y′′−5xy′+13y=2x3 NOTE: Write your answer clearly in...
The demand for cat food is given by D(x)=110e^−0.02x where x is the number of units...
The base of a solid is the region bounded by y = 9 and y =...
made a mistake cancel question
Find the area of the "triangular" region in the first quadrant that is bounded above by...
A small company of science writers found that its rate of profit (in thousands of dollars)...
A box with an open top is to be constructed from a square piece of cardboard,...
1. A trail of ants on a silo is described by the helix ?: ?⃗(?) =...
Choose one of the following statements to discuss the validity of the statement . if the...
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