# 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)
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

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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