CPhill

d) lim x→3 [1/(x-3) - 9/(x² - 9)]  Notice that this simplifies to

lim x→3 [(x - 6)/(x² - 9)] 

Note that when

x → 3^- .... [x - 6)/(x² - 9)] →  ∞   and when x → 3⁺  [x - 6)/(x² - 9)] →  - ∞

Thus .......lim x→3 [x - 6)/(x² - 9)]   =  d.n.e.

e)  lim x →∞ [(3 - cosx)/ (x² + 10)] .......note that we can write this as

lim x →∞ [(3 / (x² + 10)] - lim x →∞ [( cosx)/ (x² + 10)]

The first is easy.... it just evaluates to 0

For the second, note that

-1 ≤ cosx ≤ 1      and dividing everything by x² + 10, we have

[-1/x² + 10] ≤ [cosx/x² + 10]  ≤ [1/x² + 10]

Note that, as the two outside functions appproach infinity, they both approach 0. So, the middle function is "Squeezed" and it approaches 0, as well.

Therefore......  lim x →∞ [(3 - cosx)/ (x² + 10)]  =  0

f) lim x→∞ e ^{[(x+ 1)/(2x^2 + 1)]}

This one is easy....note that.... lim x→∞ [(x+ 1)/(2x^2 + 1)] = 0

So ....lim x→∞ e ^{[(x+ 1)/(2x^2 + 1)]}  =  lim x→∞ e⁰  = 1

I'm not great at limits......but  I think these might be correct.....

antilog 2.1705 = 10 ^2.1705 = about 148.08123

Thanks for that, geno.......I see that your answer is what they were looking for.....

If the product of a number and -3 is reduced by 5 the result is 25 less than twice the opposite of the number. Find the number.

OK.......mathematically, we have

[N(-3) - 5] + 25 = 2(-N)     simplify

-3N + 20 = -2N                add 3N to both sides

20 = N    

I assume you might want to convert 79 radians to degree measure

Use this:

79 * 180/pi = 4526.36658°

To convert this to an angle in the interval [0, 360]  divide the answer by 360 = 12.5732405

Subtract the integer part and multiply the decimal part by 360 = .5732405 * 360 = about 206.37°

-7x-3x+=-8x-8        simplify on the left

-10x = -8x - 8         add 8x to both sides

-2x = -8                 divide both sides by -2

x  = 4

5x² + 20x

The greatest number that divides 5 and 20 is 5

And the greatest common factor between x² and x is x

So we  have.......

5x(x + 4)

Subtract the x's and square this value.....[6 - (-3)]² = 9² = 81

Do the same thing with the y's [5 - (-8]² = 13² = 169

Add these values and take the square root ......  81 + 169 = 250.......√250 = 5√10

That's it !!!

The sides of the room are 16 ft each.....so the number of square feet is just 16² = 256 ft²

So 256 ft² x $10 per square foot  = $2560