# MATH 2301-102 Fall 2018 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?