Calculus Answers

Check whether the function: f: R^2→R, defined by

f(x,y)= x+ysinx has extremum at any point in the domain of f.

find an equation of the line tangent to the curve y=3x²-1 and parallel to the line 2x-y+3

Find the minimum value of the function 

f(x, y) = x²+ 2y²on the circle x² + y²= 1. 

Determine all the points on the curve

y = 2x ^ 3 + 3x ^ 2 - 18x + 3 where the slope of the tangent line is -6.

does the series ∑ 1/n⋅[1+(ln n)²] converge or diverge

n=1 below ∑

∞ on top of ∑

Determine the elements of the following sequence

1. A=n^2-3n+3 where: 4<n<8

2. B = n (-1) ^n where: 2<n<4

Match the parametric equations to the shape of their graphs.

x = 2t + 1

y = 1 - t

shape:

x = t - t²

y = 1/2(t -3)

shape:

x = cos(t)

y = sin(t)

shape:

x = t² - 1

y = sin(t)

shape:

When is the graph of the parametric equations in Quadrant 1?

x = 5t + 35

y = -4t + 16

The graph is in Quadrant 1 when:

_ < t < _

Eliminate the parameter to write y as a function of x:

x = √t

y = 2t - 3

The path of 2 objects are described by the parametric equations below.

object 1: 

x = t

y = t² + 2

object 2:

 x= 2t +1

y= t + 4

Find when and where the objects collide.

They collide at (_,_) when t = 

.