Chapter 1

1.1 A Preview of Calculus

100

Determine whether the problem can be solved using precalculus or calculus: Find the distance traveled in 15 seconds by an object moving with a velocity of v(t)=20+7 cos t

What is Precalculus

200

Find the are of a circle that center lies at (-2,1) and has outside point at (-1,0)

2π

300

Find the volume of a cylinder that has a radius for 3 and a height of 6

What is 54π

400

When estimating the length of a curve you can divide the curve into line segments than by finding the length of those segments you can estimate the length. Describe how you could continue this process to get a more accurate approximation of the length of the curve

What is adding more line segments

500

Describe how you might estimate the area underneath a curve without calculus 

What is by dividing the area underneath into rectangles the finding the area of those and adding them

1.2 Finding Limits

100

List the x values you would look at while using a table to estimate the limit as x approaches 6

What is 5.99, 5.999, 5.9999, 6, 6.0001, 6.001, 6.01

200

State one of the three reasons why a limit might not exist

What is Behavior differs from the right and left, it is unbound, or oscillates

300

Find the Limit if it exists

Lim_x->5|x-5|/(x-5)

(Graphing Utility Allowed)

What is does not exist

400

Informal Defintion of a limit

What is f(x) become arbitrarily close to L

500

Actual Definition of a limit 

What is for each ε>0 there exist a δ<0

1.3 Evaluating Limits

100

Use a graphing utility to graph the function and visually estimate the limit

lim_x->-1=x²-5x

What is 6

200

Determine the limit visually

lim_x->-1=(-2x²+x)/x

What is 3

300

Find the Limit

lim_x->14-x²

What is 3

400

Find the Limit

lim_x->4(√(x+5)-3)/(x-4)

What is 1/6

500

Find the Limit of the trigonomic function if it exists

lim_x->5π/6 sin x

What is 1/2

1.4 Continuity and One Sided Limits

100

Determine the continuity of the function

f(x)=1/(x²-4)

(Graphing Utility Allowed)

What is Discontinuous at x=-2 and x=2 

200

Determine the continuity of the function on the closed interval

g(x)=√(25-x²), [-5,5]

What is continuous

300

Find the removable discontinuity of the function

f(x)=(x+2)/(x²-3x-10)

(Graphing Utility Allowed)

What is removable discontinuity at x=-2

400

determine the continuity of the composite function h(x)=f(g(x))

f(x)=1/(x-6)

g(x)=x²+5

(Graphing Utility Allowed)

What is nonremovable discontinuities at x=1 and x=-1

500

True or False If f(x)=g(x) for x≠c and f(c)≠g(c), then either f or g is not continuous at c

What is true

1.5 Infinite Limits

100

Using the Given equation determine whether f(x) approaches infinity or negative infinity as x approaches -2 from the right

2|x/(x²-4)|

(Graphing Utility Allowed)

What is positive infinity 

200

Find the Limit if it exists

lim_x->1+(2+x)/(1-x)

(Graphing Utility Allowed)

What is negative infinity

300

Find the vertical asymptotes of the function

h(x)=(x²-2)/(x²-x-2)

What is x=2 and x=1

400

Determine if the equation has a vertical asymptote or a removable discontinuity 

f(x)=(x²-1)/(x+1)

What is a removable Discontinuity at x=-1

500

Find the Limit

lim_x->-3-(x²+2x-3)/(x²+x-6)

What is 4/5