Recent content by npellegrino

This is what I have so far. I believe i use this rule d/dx log a ^ u = 1/(lna)u so ln = 1 a = ln u = (1+e^sqrtX)/(2-e^cosx) now i need to take the derivative of u, does e^sqrtX = e^sqrtX or is it e^sqrtX * derivative of sqrtX making it e^sqrtX * 1/2sqrtX d/dx u =

I am having difficulty figuring this one, any guidance will be appreciated.

Yes, 2 was tricky, it's the factors of the sum that are only even. But would I consider all 36 sums or only the 12 (2,3,4,5,6,7,8,9,10,11,12) hmmm

Draw a table for throwing two dice (one red one blue). Find the probability. 1. That the sum is divisible by seven 2. The sum has factors whose sum is even 3. The sum is a composite number. My solutions: 1. 1/6 2. 7/11 3. 7/12 Work is attached: Any advice would be great. Thanks...

Also i believe the 3rd problem is 21/36

I am questioning my solution for the 2nd problem, wouldn't it be 7/11 since there are only 11 possibile sums (2,3,4,5,6,7,8,9,10,11.12) and the factor's sums are only even for (3,5,6,7,10,11,12)? I attached my work below.

Draw a table for throwing two dice (one red one blue). Find the probability. 1. That the sum is divisible by seven 2. The sum has factors whose sum is even 3. The sum is a composite number. My solutions: 1. 1/6 2. 7/36 3. 31/36 Any advice would be great. Thanks in advanced.

Critical numbers are -1/3 and -1/2

Find all critical numbers if any. I found the critical number -1/3 , just checking my work. Any input would be great. the function f(x) = x*sqrt2x+1 f'(x) = (3x+1)/sqrt2x+1 3x+1 = 0 , x = -1/3

Alright i think i solved it... finally thanks for the help i really do appreciate it from you 2 :)f(4) = -6 f(0) = 0 which gives me -6/4 the derivative 1/2sqrtX -2 = -6/4 which will give me 1/2sqrtx = 1/2 then x = 1

f(4) = sqrt4 - 8 = -6 f(0) = sqrt0 - 2(0) = 0

Alright I'm having a brainfart i see what you are saying.

maybe my professor has taught me wrong?

You are not taking the derivatives of f(b) and f(a)... the mean value theorem states that if f is continuous on the closed intervals [a,b] which in this case is [0,4] and differentiable on the open interval (a,b,) then there exists a number c in (a,b) such that

the derivative i got for f(x) is 1/2sqrtX - 2 then i set that equals to (f(b)-f(a))/b-a which is 1, so I'm trying to figure 1/2sqrtX - 2 = 1 and I'm having trouble figuring the fraction