A few Pre-Calc problems in my AP Calc summer packet

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Aug 30th 2010, 02:57 PM
INeedMathHelp33

A few Pre-Calc problems in my AP Calc summer packet

Hey guys, my teacher said we could get help from anywhere and I figured this would be a good place.

1. Let f(x) = 2x-3 [x less than or equal to 2] and x^2 + a [x greater than 2]

Sketch the curve and find the value of "a" so that lim f(x) as x->2 = 1. I guess just find the value of "a" :p

2. A piece of cardboard measures 20 by 35 inches. Two equal squaares are removed from the corners of a 20 inch side. Two equal rectangles are removed from the other corners so that the tabs can be folded to form a rectangular box with a lid.

a. Write the forumla v(x) for the volume of the box.
b. Fidn the domain of V for this problem. Express in interval notation (don't worry about end points)
c. Find the maximum volume and the value of x that gives it. Justify your work.

3. Find the solution(s) for the following system. Express your answer correctly to three decimal places (use your calculator).

f(x)= (1/4) + sin((pi)(x))
g(x)= 4^(-x)

4. Let W(t) =95sqrt(t)(sin^2)(t/6). Find W(7) and W(10). For what value of "t" is W(t)= 0?

Thanks.
Aug 30th 2010, 03:06 PM
pickslides

Have you tried these yourself?

Please show your workings.
Aug 30th 2010, 03:15 PM
INeedMathHelp33

For the first one I graphed the 2x-3 part and have tried both positive and negative values for a. Nothing makes the limit as x approaches 2 = 1. Also, is there another way to solve it without graphing?

For #2, I know the height is equal to x. The width is equal to 20-2x. I don't know what to put for the last one. I put 35-x-y but it didn't work for me.

#3. I graphed it on my calculator. I need to look for where the two lines intersect, right?

#4. I've never seen a problem like this and I'm not the greatest at functions. So no, I haven't attempted this last one (Crying)
Aug 30th 2010, 03:40 PM
pickslides

Quote:

Originally Posted by INeedMathHelp33

Hey guys, my teacher said we could get help from anywhere and I figured this would be a good place.

1. Let f(x) = 2x-3 [x less than or equal to 2] and x^2 + a [x greater than 2]

Sketch the curve and find the value of "a" so that lim f(x) as x->2 = 1. I guess just find the value of "a" :p

With (2,1)

$\displaystyle f(x)= x^2+a$

$\displaystyle 1 = f(2)= 2^2+a\implies a=-3$

Quote:

Originally Posted by INeedMathHelp33

2. A piece of cardboard measures 20 by 35 inches. Two equal squaares are removed from the corners of a 20 inch side. Two equal rectangles are removed from the other corners so that the tabs can be folded to form a rectangular box with a lid.

a. Write the forumla v(x) for the volume of the box.
b. Fidn the domain of V for this problem. Express in interval notation (don't worry about end points)
c. Find the maximum volume and the value of x that gives it. Justify your work.

I think you are looking for

$\displaystyle v(x) = x(35-2x)(20-2x)$

Quote:

Originally Posted by INeedMathHelp33

3. Find the solution(s) for the following system. Express your answer correctly to three decimal places (use your calculator).

f(x)= (1/4) + sin((pi)(x))
g(x)= 4^(-x)

Yep calculator is best for this one.

Quote:

Originally Posted by INeedMathHelp33

4. Let W(t) =95sqrt(t)(sin^2)(t/6). Find W(7) and W(10). For what value of "t" is W(t)= 0?

Thanks.

$\displaystyle W(7)= 95\sqrt{7}\times \sin ^2\frac{7}{6}= \dots $

$\displaystyle W(10)= 95\sqrt{10}\times \sin ^2\frac{10}{6}= \dots $

$\displaystyle W(t)= 0 \implies 0= 95\sqrt{t}\times \sin ^2\frac{t}{6}$ This is another job for your calculator.