Grab Bag (Day 1)

Problem 1

Find (∫_0^1)(tan^(-1))(x)dx

Problem 2

Find the tangent plane to z=(x^3)y-(y^2) at the point (2,1,4)

Problem 3

Find the tangent line to (x^4)+x y +(y^3)=11 at the point (1,2).

Problem 4

Find the interval of convergence for the real series (Underoverscript[∑ , (n=1), ∞])((((x+3))^n)/((2^n)(Sqrt[n])))

Problem 5

Given that x=1 and x=3-i are solutions to (x^4)-(x^3)-26(x^2)+86x-60=0, find the other solutions.

Problem 6

Find ∫(Sqrt[(x^2)-4])dx, where x>2.

Problem 7

Solve sin(x)+cos(x)=1 over the real numbers.

Problem 8

Find sin(2(tan^(-1))((5/12))).

Problem 9

Find the maximum value of (sin^2)(x)+cos(x) on the interval [0,2π].