Suppose you park your car at a trailhead in a national park and begin a 2-hr hike to a lake at 7 A.M​​. on a Friday morning. On Sunday morning, you leave the lake at 7 A.M. and start the 2-hr hike back to your car. Assume the lake is 3 mi from your car. Let f(t) be your distance from the car t hours after 7 a.m. on Friday morning, and let g(t) be your distance from the car t hours after 7 a.m. on Sunday morning.

a. Evaluate f(0), f(2), g(0), and g(2).

Suppose you park your car at a trailhead in a national park and begin a 2-hr hike to a lake at 7 A.M​​. on a Friday morning. On Sunday morning, you leave the lake at 7 A.M. and start the 2-hr hike back to your car. Assume the lake is 3 mi from your car. Let f(t) be your distance from the car t hours after 7 a.m. on Friday morning, and let g(t) be your distance from the car t hours after 7 a.m. on Sunday morning.

b. Let h(t)=f(t)−g(t). Find h(0) and h(2).

Let g(x)= {1 if x≥0

−1 if x<0.

a. Write a formula for |g(x)|.

Find the horizontal asymptotes of each function using limits at infinity.

f(x) = (2e^x + 3) / (e^x + 1)

Sketch a graph of y=2^x and carefully draw three secant lines connecting the points P(0, 1) and Q(x,2^x), for x=−3,−2, and −1.

Find the horizontal asymptotes of each function using limits at infinity.

f(x) = (3e^5x + 7e^6x) / (9e^5x + 14e^6x)

Even function limits Suppose f is an even function where lim x→1^− f(x)=5 and lim x→1^+ f(x)=6. Find lim x→−1^− f(x) and limx→−1^+ f(x).

Evaluate lim x→1 3√x − 1 / x (Hint: x−1=(3√x)^3−1^3.)

Find functions f and g such that lim x→1 f(x)=0 and lim x→1 (f(x)g(x))=5.

Find constants b and c in the polynomial p(x)=x^2+bx+c such that lim x→2 p(x) / x−2=6. Are the constants unique?

Suppose g(x)=f(1−x) for all x, lim x→1^+ f(x)=4, and lim x→1^− f(x)=6. Find lim x→0^+ g(x) and lim x→0^− g(x).