MATH 155 EXAM 1 REVIEW

Functions

100

Find the domain of the function. f(x)= 4(x-1)^-1/2

Domain: (-infinity,1) U (1,infinity) 

200

What are the domain and range of the function? f(x)= 7-(9-2x)^1/2

domain= (-infinity, 9/2] 

range= (-infinity, 7] 

300

Let f(x)= 2x²-x. Find f(x+h)-f(x). 

4xh+2h²-h

400

Determine h(2). Where h= g(f(x)). f(x)= x+1 g(x)= 2(x²-1)

16

500

What is a function? 

a function must have 1 singular output for every output

or

cannot have two of the same y-values

Limits

100

Lim x-->2 (x²-4)/x-2

4

200

Lim x--> infinity (24x⁴+13x³-1,020)/(8x⁵-40x⁴+30x³+10,450)

0

300

Lim x--> -1 (1)/(x+1)

DNE b/c LHL does not equal RHL 

400

Lim x--> 3 (x(x²+7)^1/2)/(2x-(2x+3)^1/2)

4

500

Let f(x)= 

(x²-4)/ x+2 x cannnot = -2 

k x= -2

Find the value of k that will make the function continuous. 

-4

Word Problems

100

A manufacturer has a monthly fixed cost of $20,000 and a production cost of $10 for each unit produced. The product sells for 415/unit. Let x represent the number of units produced. What is the cost function? 

C(x)= 10x+ 20,000

200

Find the slope of the tangent line to f(x). f(x)= pie/2x² when x= pie. 

1/pie²

300

TuffStuff Inc. manufacturers steel backpacks. The weekly cost for producing x backpacks is given by the C(x)= 8000 + 100x. 

Find the marginal cost function. 

C'(x)= 100 

400

Find the equation of the tangent line when x=2. f(x)= x²/ x+2 

y= 3/4x -1/2

500

Find f'(x) using the limit definition of a derivative. f(x)= -4/x²

8/x³

Derivatives

100

Find f'(x). f(x)= (3x²=7)(4x³+1)

(6x)(4x³+1)+(12x²)(3x²-7)

200

Find f'(x). f(x)= (x)^1/3 + (1/(x)^3/4)

(1/3(x)^2/3) - (3/4(x)^7/4)

300

Find f'(x). f(x)= 2/(x²-1)⁴

-16/(x²-1)⁵

400

Find f'(x). f(x)= (1-x³)^1/3

-x²/ (1-x³)^2/3

500

Find f''(x). f(x)= (x²+1)^1/2

1/(x²+1)^1/2 - x²/ (x²+1)^3/2