For Exercises 19-30, the initial substitution of x = a yields the form 0/0. Look for ways to simplify the function algebraically, or use a table or graph to determine the limit. When necessary, state that the limit does not exist. lim x → − 3 2 x 2 − x − 21 9 − x 2
For Exercises 19-30, the initial substitution of x = a yields the form 0/0. Look for ways to simplify the function algebraically, or use a table or graph to determine the limit. When necessary, state that the limit does not exist. lim x → − 3 2 x 2 − x − 21 9 − x 2
Solution Summary: The author calculates the value of the expression undersetxto -3mathrmlim2.
For Exercises 19-30, the initial substitution of
x
=
a
yields the form 0/0. Look for ways to simplify the function algebraically, or use a table or graph to determine the limit. When necessary, state that the limit does not exist.
An airplane flies due west at an airspeed of 428 mph. The wind blows in the direction of 41° south of west
at 50 mph. What is the ground speed of the airplane? What is the bearing of the airplane?
428 mph
41°
50 mph
a. The ground speed of the airplane is
b. The bearing of the airplane is
mph.
south of west.
Rylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach
one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck
starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a
horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate
a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The
angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude
and its direction angle from the positive x-axis.
119 lb
20.2°
377 lb
a. The resultant force is
(Tip: omit degree notations from your answers; e.g. enter cos(45) instead of cos(45°))
b. It's magnitude is
lb.
c. It's angle from the positive x-axis is
Find a plane containing the point (3, -3, 1) and the line of intersection of the planes 2x + 3y - 3z = 14
and -3x - y + z = −21.
The equation of the plane is:
Chapter 1 Solutions
Calculus and Its Applications, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)
Elementary Statistics: Picturing the World (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.