### Find the following limits as x approaches infinity: x ^ (1/x).

Find the following limits as x approaches infinity: 1) x ^ (1/x) (1/x) is the exponent. It may be easier to read in the attached Word doc.

Explore BrainMass

- Anthropology
- Art, Music, and Creative Writing
- Biology
- Business
- Chemistry
- Computer Science
- Drama, Film, and Mass Communication
- Earth Sciences
- Economics
- Education
- Engineering
- English Language and Literature
- Gender Studies
- Health Sciences
- History
- International Development
- Languages
- Law
- Mathematics
- Philosophy
- Physics
- Political Science
- Psychology
- Religious Studies
- Social Work
- Sociology
- Statistics

Find the following limits as x approaches infinity: 1) x ^ (1/x) (1/x) is the exponent. It may be easier to read in the attached Word doc.

50 Problems Please see the attached files for the fully formatted problems.

Find the zero of the linear function f(x)=3x-12 Find the zeros of f(x)=x^2-2x-3 Find the vertex of f(x)=x^2-2x+4 Find the axis of symmetry of f(x)=x^2-2x+4 Find the zeros and state the multiplicity of each for f(x)=x^2(x+3)(x+1)^4 Find the zeros of f(x)=x^2-8x+12

1.) A deposit of S dollars that earns 100r% annual interest compounded continuously leaves a balance of P = 'Se' power of 'n' or ( 'Se' to the 'n') dollars after "t" years. a) What will an amount of $ 5000 grow to after 15 years at 10% annual interest compounded continuously? b) Determine the rate at which P is growi

Question (1): Find the equation of the plane containing the vector a = (3 , - 2 , - 1 ) and parallel to the vectors b = (1, - 2 , 4 ) and c = (3 , 2 , - 5 ) Question (2) : Find the equation of a plane passing through A and B whose position vectors are 4i + j - 2k , 5i + 2j + k respectively and parallel to the vector 3i

#(d^3z/dx^3) - 3(d^z/dx^2) + 2(dz/dx) = e^3x/(1 + e^x)

Question (1) a = (3 , 1 , 2 ) , b = ( - 1 , 1 , 0 ) , c = ( 0 , 0 , - 4 ) , then show that a × ( b × c ) ≠ (a × b) × c Question(2) Given P ( 2 , 1 , 5 ), Q = ( - 1 , 3 , 4 ) and R = ( 3 , 0 , 6 ), then find (a) a vector orthogonal to the plane through the points P,Q and R (b) Find the area of the triangle PQR

Determine whether the given vectors are orthogonal, parallel or neither. <-5,3,7> and <6,-1,2> <4,6> and <-3,2> -i + 2j + 5k and 3i + 4j - k 2i + 6j - 4k and -3i -9j +6k Find a unit vector that is orthogonal to both i+j and i+k. If a = <3,0,-1>, find a vector b such that comp_a b = 2 (component of b in the a direction

1. y'' + k*y = 0 BC: y'(0) = 0 y'(L) = 0 2. y'' + k*y = 0 BC: y(0) = y() y'(0) = y'() 3. y'' + k*y = 0 BC: y(0) = 0 y() +2*y'() = 0 4. y'' + 2*y' + (1+k)*y = 0 BC: y(0) = y(1) =0 Please see the attached file for

1.) Let f(x)=(the integral from 0 to x^2) sint dt. At how many points in the closed interval [0, square root of pi] does the instantaneous rate of change of f equal the average rate of change of f on that interval. keywords: integration, integrates, integrals, integrating, double, triple, multiple

Please explain how/why: lim x---> - 1 x^2 - 1 / x+1 How would this change if the 1 was positive?

1) a = (1, 2, -2); ||b|| = 6. What choice of b will make the dot product a . b the least possible? 2) The plane P pass through the point M (2, 3, 1) and is parallel to vectors u = (1, -1, 4) and v = (2, 1, 0). Find the distance from the point N (3, 2, 4) to the plane P. 3) Find an equation of the plane that passes through (1,

1) Find the equation of the line passing through the point (6, 1, 8) in the direction of the vector (-3, 4, -2). Write the equation in vector and coordinate form. 2) Find the equation of the line segment joining points (2, 4, 6) and (1, 7, 8), both in vector and coordinate form. Be sure to specify the set of possible values o

Determine the infinite limit #1)lim x-1/x^2(x+2) x->0, #2)lim csc x x->pi -, #3)lim ln(x-5) x->5+, #4)lim 6/x-5 x->5- #4) The slope of the tangent line to the graph of the exponential function y= 2^x at the point (0,1) is limx->0(2^x - 1)/x. Estimate the slope to three decimal places. keywords : find, findi

Find limit lim x---> - 4 x^2 - 16 / x+4 Please explain keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving

4. A retailer you spoke with in New York City's fashion district imports haute couture from European designers. One of the accommodations which must be considered when importing fashion from other countries is the difference in the size charts. A function that will convert dress sizes in the United States to those in Italy is

If y = XsinX prove that Y (X^2 + 2) - 2X dy/dx + X^2 d2y/dx2 = 0

(a) The function 1/t is continuous on the given interval, therefore integrable. The primitive is log(t). The primitive of exp(t) is exp(t). Therefore the integrals are: (b) The primitive of -cos(x) is -sin(x) anf the primitive of x is x2/2, therefore the integral equals: (c) We apply the so called Simpson's approximation:

Find the general solution to the following (d^4y/dx^4) + 4(d^3y/dx^3) + 8(d^2y/dx^2) + 8(dy/dx) + 4y=0

Find the general solution of the following (d^6y/dx^6) -3*(d^4y/dx^4) +3*(d^2y/dx^2) -y=0

Let s (n)= (sigma sign with n as upper bound and i=1 as lower bound) (1+(i/n))^2 * (1/n). Find the limit of s (n) as n approaches positive infinity.

Use the fundamental theorem of calculus to evaluate: (integral from 0 to 2) abs(x-1)*dx

Question: Evaluate the limit of e^(-x)*ln[x] as x approaches positive infinity. Please show all work.

Use power series to solve the second-order homogeneous equation : u''(t) - tu'(t) - 2u(t) = 0

A particle of mass m moves under the influence of constant force f and the friction force γ(xdot)n Its equation of motion reads: m(x-double dot) + γ(xdot)n = f Find x(t) for n=1 and n=2 if x=0 and x-dot=0 at t=0 Check that your solutions exhibit the correct behavior in the limit. Please see the attac

4. Find the center, vertices and foci of 4x^2 + 9y^2 -8x +36y +4 =0. Graph, labeling all relevant points including the foci. 5. Find the equation of the hyperbola whose center is the origin, vertex at (2,0) and focus at (3,0). Write the equation of the asymptotes. 6. Find the center, vertices, foci and asymptotes

F(x,y)=1/(x^2+y^2) Is the domain (-infinity, 0) union (0, infinity)? Is the range (0, 1]? What are the x and y intercepts and is the z intercept undefined?

How do you find the x, y, and z-intercepts of a 3-Dimensional graph step by step? I am trying to interpret some graphs and would like this information to assist me in the interpretation. keywords: 3D, 3Dimensional

2. A spring with a 4-kg mass has natural length 1 m and is maintained stretched to a length of 1.3 m by a force of 24.3 N. If the spring is compressed to a length of 0.8 m and then released with zero velocity, find the position of the mass at any time t. 10. As in Exercise 9, consider a spring with mass m, spring constant k,

Find the length of an Archimedian spiral r=x, for 0<= x <= 2pi