# Solving Inequalities, Limits and Derivatives

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Solve the following inequalities/equations expressing the solution. Show all work and box the final answer.

Write an equation for the line described below.

Graph the following function. What symmetries, if any, does the graph have?

Find the value that lim g (x) must have if the given limit statement holds.

Are there any points on the curve y = (x/2) + 1/(2x -4) where the slope is -3/2? If so, find them.

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MATH 30102 - CALCULUS & ANALYTIC GEOMETRY (Thomas)

Solve the following inequalities/equations expressing the solution. Show all work and box the final answer.

1) 5x - 3 7 - 3x

Rearragne the equation so that items with x on the left side, and the constants are the right side.

The solution is

2) 3 - < ½

First, the abosolute can be rewritten as

For ,

(1)

For

(2)

x satisfy the above equation, that is (3)

The reason I ddin't solve the inequailities (1) and (2) seperately is that you have to analyze the cases of x>0 and x<0 seperately.

With (3), it is obvious that x>0. Given x>0

When

(4)

When

(5)

So the solution is

3) ( x - 1 ) 2 < 4

There are two cases: (1)

, which is impossible.

(2)

The solution is

Write an equation for the line described below.

4) Passes through ( -1, 1 ) with solpe -1

Assume the equation of the line is . We know the slope is m=-1, so the equation is . Now the line is throught (-1, 1), so substitute into the line equation,

So the line equatin is

5) A particle starts at A ( -2, 3 ) and its coordinates change by increments x = 5,

y = - 6. Find its new position.

The starting x-position is , so

The starting y-position is , so

Sot the ...

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Solving Inequalities, Limits and Derivatives are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.