MATH 2301-102 and -103 Fall 2017 Calculus I Recitation 1 Week 1

See the coversheet for instructions and the point value of each problem.

    1. Write the equation of the line with slope 2 that passes through the point \((1,-7)\).
    2. Solve the equation \(|2x+1|=3\).
    3. Solve the inequality \(|x^2-9| \ge 6\).
  1. Given \(p(x) = x^3 +6x^2-9x-14\),
    1. Completely factor \(p(x)\), using the fact that \(p(2)=0\) to help you.
    2. Sketch a graph of \(p(x)\) and label the points where the graph intersects the \(x\)-axis and the \(y\)-axis.
  2. Simplify \[\frac{5(x+h)+(x+h)^2-(5x+x^2)}{h} \,.\]
    1. Solve the inequality \( e^{7x-8} \ge 2\) and express your answer in interval notation.
    2. Solve the equation \(\log_6(x+4)+\log_6(3-x)=1\) and express your answer in set notation.
  3. Given that \(\csc(\theta) = 11\) with \(\theta\) in the second quadrant, find the exact values of all six trigonometric functions evaluated at \(\theta\):
    1. \(\sin(\theta)=\)
    2. \(\cos(\theta)=\)
    3. \(\sec(\theta)=\)
    4. \(\csc(\theta)=11\)
    5. \(\tan(\theta)=\)
    6. \(\cot(\theta)=\)
  4. A superhero, standing on the ground, launches 50 feet of wire from a grappling gun, held at an angle of elevation of \(\pi/3\) radians. The grapple hits and catches the top edge of the building.
    1. How tall is the building?
    2. How far from the base of the building is the superhero standing?

Last modified: Thu Aug 17 19:23:48 UTC 2017