Math 180 Review

Chapter 1

100

lim (7x-21)/(x^2-9)

x=3

7/6

200

lim (square root of x+7)-3/(x^2+2x-8)

x=2

1/36

300

solve sec^2x+3secx=-2

pi, 2pi/3, 4pi/3

400

f(x)={x^2+x-2     x<1

        {5/x             x>= 1

find lim as x approaches 4 and limit as x approaches 1

5/4 and 0&5

500

sketch y=4sin(3x)

show later

Chapter 2

100

discontinuity for f(x)= (3)/(x-4)  x<2

                                6x+1        x>= 2                       

jump 

200

lim   5x-8=7  E=.2

x=3

delta= .04

300

lim  5x-8=7

x=3

E/5

400

lim 3x+1=6

x=2

no answer

500

lim   (5)/(x-4)²=infinity

x=4

square root of 5/n

Chapter 3

100

derivative of X^2-3x+7 and slope of tangent line at -5

-13

200

lim (cosh-1)/h

h=0

0

300

y= sinx+3tanx

No solution

400

f(x)=5cotx +(3cscx)/2

-.5cscx(10cscx-3cotx)

500

find equation of tangent line (-1,-1) for

x⁴y-xy³=-2

y=(-5/4)x-(9/4)

Chapter 4

100

A 20 ft ladder is leaning against a wall. The base is 8 ft from the wall. Push the bottom of the ladder toward the wall at 1ft/sec. How fast is the ladder moving up the wall 5 sec after we start? 

.152

200

Use linear approx for 1/-.8

-.2

300

find mins and maxs for f)x)=x⁴-8x³+7

local min at (6,-425)

400

Use rolles thm for F(x)= (x²+8)/(3x-4) [-6,0]

(4-2square root of 22)/(3)

500

lim     x²lnx

x=0⁺

0