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Calculus Questions
Find a power series representation for the function. (Give your power series representation centered at x=0x=0.)...
Find the tangent plane to the surface z = cos(xy) when (x, y) = (π, 0).
Use the appropriate chain rule to find ??/?? and ??/?? if ? = ?^2 + ?^2...
f(x)=x3-6x2+9x+2 on interval [2,4] Find any local and absolute extreme values of the function on the...
Find the tangential and normal components of the acceleration vector. Then find the speed of the...
Find the derivative of the function. h(t) = (t + 4)2/3(3t2 − 2)3
Find the curvatures of the given curves. i: r(t) = ⟨t, t2/2, t2⟩ ii: r(t) =...
Set up, but do not evaluate, the integral for the volume of the solid obtained by...
Curve given below, find the vectors T, N, and B at the point given. r(t) =...
Determine whether the given vectors parallel, orthogonal, or neither. If they are neither parallel nor orthogonal,...
f(x)=4x^3+9x^2−12x−3. 1.Find the interval(s) on which f is increasing. Answer (in interval notation): 2. Find the...
Find the parametric and symmetric equations of the line that is parallel to the line x...
Minimizar f(x,y,z)=x2+4y2+16z2 sujeto a la restricción. Minimize f(x,y,z)=x2+4y2+16z2 subject to the constraint 1=xyz 1=xy 1=x
Find f. f ''(x) = 6 + 6x + 36x2, f(0) = 3, f (1) = 13
Verify that the Divergence Theorem is true for the vector field F on the region E....
Solve the differential equation dy/dx + 4(x^3)y = 8(x^3)
Find the equations of (i) the tangent plane and (ii) the normal line to the surface...
A full rectangular swimming pool with an 18 x 12 feet base and a depth of...
a. Find the first three terms in the power sereis for integral from 0 to x,of...
Find the area of the surface generated by revolving the curve x = ?square root 4y...
Find the centroid of the region bounded by the graphs of the functions y=3x^2, y=x^2+7 The...
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with...
1) Find the maximum and minimum values of the function y = 13x3 + 13x2 −...
A corporation is initially worth 88 million dollars and is growing in value, VV, by 3434%...
In the system AX=b, where A is m x n matrix and rank of A is...
Suppose that a function f has the the following limits. What is true about the graph of...
Find the exact area of the surface obtained by rotating the curve x = 1-2y^2, 1...
Suppose that 5 J of work is needed to stretch a spring from its natural length...
Find an equation of the plane.The plane through the point (6, −5, −1) and parallel to...
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 350...
Find absolute maximum -X^3+3X^2-4 at (-2,1)
Find the absolute maximum of h(x)= x^2 −x−2 over [−3,6]. Enter only the y -coordinate of...
Find an equation of the tangent plane to the surface z = x^2 + xy +...
Use implicit differentiation to find ∂z/∂x and ∂z/∂y if yz + xlny = z^2 .
A trough is filled with a liquid of density 810 kg/m3. The ends of the trough...
A milk truck carries milk with density 64.6 lb/ft3 in a horizontal cylindrical tank with diameter...
Please show all work step by step The growth of a bacterial colony is modeled by...
Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 8...
1. A volume is described as follows: 1. the base is the region bounded by y=2−...
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...
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