# Calculus

Question #1

Evaluate exactly

0

lim

→

(1 + )

2

Question #2

Find the equation of the line that is tangent to = 2 and is perpendicular to the line

3

( + 1)

=− (9) + 2. Leave your answer with exact values

Question #3

A particle moves back and forth along a straight line. Its position (in meters), relative to the

origin, at any time t (in seconds) is given by () = 3 . Find the total distance

3 − 9

2

+ 5 − 15

travlled during the first ten seconds. (Remember to include units)

Question #4

When does () = ( + 2), 0 < < 2π have a local minimum?

Question #5

Find the intervals where the function () = 2 + is concave up

1

2

2, 0 ≤ ≤ 2π

Question #6

A rectangle is inscribed with its base on the x axis and its upper corners on the parabola

=− 4 . Find the dimensions of the rectangle with the greatest possible area

2

+ 12

Questions 2

The difference of the tens and the ones digits of a two-digit number is 3. The number is sixteen times the digit in its ones place. Find the number