1. Assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve the triangle, if possible. Round your answers to the nearest tenth. (If not possible, enter IMPOSSIBLE.)

α = 36°, γ = 70°, a = 35

2. Assume α is opposite side a, β is opposite side b, and γ is opposite side c. Solve the triangle, if possible. Round your answers to the nearest tenth. (If not possible, enter IMPOSSIBLE.)

α = 60°, β = 60°, γ = 60°

3. Use the Law of Sines to solve for the missing side for the oblique triangle. Round your answer to the nearest hundredth. Assume that angle A is opposite side a, angle B is opposite side b, and angle C is opposite side c.

Find side a when

A = 139°,

C = 27°,

b = 10.

a =

Find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic cylinders

y = 1 − x², y = x² − 1 and the planes x + y + z = 2, 5x + 2y − z + 13 = 0.

Problem 13.2: Where on the parametrized surface ~r(u; v) = [1 +
u³,v²,uv]^T is the temperature T(x, y, z) = 2 + x + 12y - 12z minimal?
To nd the minimum, look where the function f(u; v) = T(~r(u, v)) has an
extremum. Find all local maxima, local minima or saddle points of f.

Solve the given initial-value problem.

y'' + y = 0,    y(π/3) = 0,    y'(π/3) = 4

Find an equation of the plane that passes through the point (1, 7, 3) and cuts off the smallest volume in the first octant.

Translating and Solving Word Equations:

Translate then solve the algebraic equation for the following problems:

Fourteen less than 5 times a number is 1. Identify the integer.

When the sum of a number and 3 is subtracted from 10 the result is 5. Identify the integer.

The sum of two consecutive integers is 139. Find the integers.

The sum of two even consecutive integers is 46. Find the integers.

The sum of three consecutive integers is 57. Find the integers.

Find the derivative of the function.

A) f(x)=(2+x^3)^2/3

B) h(t)= (t^4-1)^9(t^3+1)^8

C) y = e^{4x sin(x)}

D) y= (x^2+2/x^2-2)^3

Consider the function f(x)=arctan [(x+6)/(x+5)] Express the domain of the function in interval notation: Find the y-intercept: y= . Find all the x-intercepts (enter your answer as a comma-separated list): x= . Does f have any symmetries? f is even; f is odd; f is periodic; None of the above. Find all the asymptotes of f (enter your answers as comma-separated list; if the list is empty, enter DNE): Vertical asymptotes: ; Horizontal asymptotes: ; Slant asymptotes: . Determine the derivative of f. f'(x)= On which intervals is f increasing/decreasing? (Use the union symbol and not a comma to separate different intervals; if the function is nowhere increasing or nowhere decreasing, use DNE as appropriate). f is increasing on . f is decreasing on . List all the local maxima and minima of f. Enter each maximum or minimum as the coordinates of the point on the graph. For example, if f has a maximum at x=3 and f(3)=9, enter (3,9) in the box for maxima. If there are multiple maxima or minima, enter them as a comma-separated list of points, e.g. (3,9),(0,0),(4,7) . If there are none, enter DNE. Local maxima: . Local minima: . Determine the second derivative of f. f''(x)= On which intervals does f have concavity upwards/downwards? (Use the union symbol and not a comma to separate different intervals; if the function does not have concavity upwards or downwards on any interval, use DNE as appropriate). f is concave upwards on . f is concave downwards on . List all the inflection points of f. Enter each inflection point as the coordinates of the point on the graph. For example, if f has an inflection point at x=7 and f(7)=−2, enter (7,−2) in the box. If there are multiple inflection points, enter them as a comma-separated list, e.g. (7,−2),(0,0),(4,7) . If there are none, enter DNE. Does the function have any of the following features? Select all that apply. Removable discontinuities (i.e. points where the limit exists, but it is different than the value of the function) Corners (i.e. points where the left and right derivatives are defined but are different) Jump discontinuities (i.e. points where the left and right limits exist but are different) Points with a vertical tangent line Upload a sketch of the graph of f. You can use a piece of paper and a scanner or a camera, or you can use a tablet, but the sketch must be drawn by hand. You should include all relevant information that has not been requested here, for example the limits at the edges of the domain and the slopes of tangent lines at interesting points (e.g. inflection points). Make sure that the picture is clear, legible, and correctly oriented.

Find the absolute maximum and​ minimum, if either​ exists, for the function on the indicated interval. f(x)=x^4+4x^3-7 (A) [-2,2] (B) [-4,0] (C) [-2,1]

Determine the radius of convergence and the interval of convergence of the following power series.

∞ ∑ n=1

(2^(1+2n))/ (((−3)^(1+2n)) n^2) (4x+2)^n .

If u(t) = < sin(8t), cos(4t), t > and v(t) = < t, cos(4t), sin(8t) >, use the formula below to find the given derivative.

d/(dt)[u(t)* v(t)] = u'(t)* v(t) + u(t)*  v'(t)

d/(dt)[u(t) x v(t)] = <.______ , _________ , _______>