MATH 155 SI PASS FINAL EXAM REVIEW

Limits

100

Find the Lim x--> infinity 

(24x⁵+13x⁴-1,020)/(8x⁵-450x⁴+30x²+10,450)

3

200

Find the Limit as x--> 1 

(x/x+1)+(3/3-x)

2

300

Consider f(x)= 

-2x+3 if x<1

x³-3 if 1 less than or equal to x less than or equal to 4 

x+1/5 if 4<x less than or equal to 9 

lim x-->1 DNE b/c LHL does not equal RHL

lim x--> 4 DNE b/c LHL does not equal RHL

400

Find the derivative using the limit defintion of a deriavtive. f(x)= x+1/x-1

lim h--> 0 -2/(x-1)²

500

Pick a value for c so that f(x) si continous everywhere f(x)= 

(2x²+2x-4/2x+4) x does not equal -2 

c  x=-2 

c=-3

Derivatives

100

Find the derivative f (3x²-7)(3x³+1)

f'(x)= 6x(10x³-14x+1)

200

Find the derivative of 2/(x²-1)⁴

f'(x)= -16x/(x²-1)⁵

300

Find the derivative of 5/3e^-7x+1

105e^-7x/(3e^-7x+1)²

400

Derive. y= ln(sqrt(x+1/3x-4))

-14/(2x+2)(6x-8)

500

Find the equation of the tangent line for y=xln(x) at x=1

y=x-1

Integrals

100

Find the integral of 

(7x³-5x+1)/(2x²)

1/2((7x²/2)-4ln|x|-1/x+C

200

Find the integral of 

x-2/cube root(x²-4x+6)

3/4(x²-4x+6)^2/3+C

300

Find the integral of... 

(e^{sqt(x) -1})/(sqrt(x))

2e^sqrt(x)-1+C

400

Given f'(x)= ln(x)/x when f(1)=-2 find f(x). 

f(x)= ln²(x)/2 +2 

500

Find the area under the curve when f(x)=4-x² on [1,-2]

9

Word Problems

100

Monsters Inc is a company that manufactures jet packs. The fixed monthly cost for each jet pack production is $120,000 and it costs an additional $1000 to produce each jet pack. The jet pack sells for $2000. Let x represent the number of jet packs produced each month. What is the profit function? 

P(x)= 1000x-120,000

200

John creates custom shoes. His montlhy cost includes $1000 for the studio space plus $25 for materials for each shoe he makes. He sells the shoes for $45 dollars each. Let x represent the number of shoes they make each month. How many shoes does John need to make each month to breakeven? 

50 shoes each month 

300

When is the function increasing? 

f(x)=  1+e^3-x

the function is never increasing, always decreasing 

400

Identify the inflection point if any. 

f(x)=x³-3x³

inflection point (1,-2)

500

Children are very expensive. I want to set up a college fund for my child to use when they go to college. I want to grow $10,000 into $100,000 in 4 years. What interest rate do I need to obtain to acheive this goal? 

r=ln(10)/4