Given v′(t)=2ti+j, find the arc length of the curve v(t) on the interval [−2,3]. You may use technology to approximate your solution to three decimal places.

a) Find the Taylor series for sinh(x) (centered at x=0), for e^x (centered at x=0) and hyperbolic sine and hyperbolic cosine.

b) same as a but cosh(x) instead

The function needs to have at least one maximum or minimum value.   

A.       Create a function that requires quotient rule (with a variable in the denominator). The function needs to have at least one maximum or minimum value.   

Please show work and guidance!

"Provide graph"

1. Find any horizontal and vertical asymptotes for this graph as well.

2.        Find the domain of f(x)

3.       Find the y-intercept f(x)

4.        End behavior: Find the limit of the f(x) as x approaches both ∞ and -∞

5.   Find the increasing and decreasing interval(s) of f(x)

6.        Find the interval(s) of concavity

7.        Find any maximum points, minimum points, or points of inflection

8.       Graph f(x) to verify that if the above answers are correct.

Solve the following initial value problem. y′′ − 10y′ + 24y  =  5x + e^(4x), y(0)  =  0, y′(0)  =  4

(not using Laplace)

Question 1: Show that x = h + r cos t and y = k + r sin t represents the equation of a circle.

Question 4: Find the area above the polar x-axis and enclosed by r = 2−cos(θ).

Question 5: If r = f(θ) is a polar curve, find the slope of the tangent line at a point (r₀,θ₀).

second order linear non-homogeneous

solve the following equations

d²y/dx²+ y=5e^x-4x²

la place transform of

1. y´´+4y´+6y_=0, y(0)=1, y´(0)=-4

2. y´+y=t^2 , y(0)=0

Find T(t), N(t), aT, and aN at the given time t for the space curve r(t). [Hint: Find a(t), T(t), aT, and aN. Solve for N in the equation a(t)=aTT+aNN. (If an answer is undefined, enter UNDEFINED.)

Function    Time

r(t)=9ti-tj+(t^2)k t=-1

T(-1)=

N(-1)=

aT=

aN=

(6) Consider the function f(x, y) = 9 − x^2 − y^2 restricted to the domain x^2/9 + y^2 ≤ 1. This function has a single critical point at (0, 0)

(a) Using an appropriate parameterization of the boundary of the domain, find the critical points of f(x, y) restricted to the boundary.

(b) Using the method of Lagrange Multipliers, find the critical points of f(x, y) restricted to the boundary.

(c) Assuming that the critical points you found were (±3, 0) and (0, ±1, find the absolute maximum and minimum of f(x, y) restricted to this domain.

What is the absolute max / min value for the function f(x) = x sqrt 1 - x on the interval [ 1 , 1 ]

Prove the transitive property of similarity: if A~B and B~C, then A~C.

Set up (Do Not Evaluate) a triple integral that yields the volume of the solid that is below

       the sphere x^2+y^2+z^2=8 and above the cone z^2=1/3(x^2+y^2)

1. Rectangular coordinates

       b) Cylindrical coordinates

       c)   Spherical coordinates

A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 4 hours. The company has only 800 work hours to use in manufacturing each day, and the packaging department can package only 300 trimmers per day. If the company profits for the cord-type model for $28.50 and the cordless model for $57.00, how many of each type should it produce per day to maximize profits? Scenario #1 (with the smaller number of cord-type trimmers): corded models cordless models Scenario #2 (with the larger number of cord-type trimmers): corded models cordless models