yeah im still not getting them... what about a definite integral from 0 to 1 e^-2x dx? substituted -2x for u, ended up with integral 0 to -2 e^u times 1/2 du, then when i evaluate i end up with -1/2 e^-2 -1, but book says (e^2 -1)/(2e^2) ?
"find any values for which is undefined 2x-4 over 4x^2+x-3"
2x-4/(4x^2 + x - 3) = 2x-4/(4x-3)(x+1)
The function is undefined when the denominator is 0, so it's undefined when 4x-3 = 0 or x+1 = 0. Solving for x gets you x = 3/4 and x = -1
"find the numerical value of 2x-3 over x^2-4x+1"
Not sure what they're asking for here, but you'd need to use the quadratic formula on the polynomial on the bottom to find out what x values make it 0.
Comments
1-e^x for the second one by similar logic. du will be -e^x, which can be subbed in for the e^x in front of the square root.
(e^-x)/(1+e^-x) ---> -du/u
e^x√(1-e^x) ------> -sqrt(u) du
Pretend there's an integral sign in front of each of them and you're good to go.
what about a definite integral from 0 to 1 e^-2x dx?
substituted -2x for u, ended up with integral 0 to -2 e^u times 1/2 du, then when i evaluate i end up with -1/2 e^-2 -1, but book says (e^2 -1)/(2e^2) ?
0-->1 e^-2x dx , u = -2x, du = -2dx, -(1/2)du = dx
-(1/2)(0 -> -2 e^u du) = -(e^-2 - 1)/2 = 1/2 - (e^-2)/2 = e^2/(2e^2) - 1/(2e^2) = (e^2 -1)/(2e^2)
Distribute the negative sign to both terms: (1- e^-2)/2
Split up the terms into two because there are two terms in the numerator: 1/2 - (e^-2)/2
edit: shit, but how do you go from 1/2-e^2/2 to e^2 / 2e^2 - 1/2e^2?
edit: ok, figured it out. thanks
2x-4 over 4x^2+x-3
find the numerical value of 2x-3 over x^2-4x+1
got a bunch more will add later
2x-4 over 4x^2+x-3"
2x-4/(4x^2 + x - 3) = 2x-4/(4x-3)(x+1)
The function is undefined when the denominator is 0, so it's undefined when 4x-3 = 0 or x+1 = 0. Solving for x gets you x = 3/4 and x = -1
"find the numerical value of 2x-3 over x^2-4x+1"
Not sure what they're asking for here, but you'd need to use the quadratic formula on the polynomial on the bottom to find out what x values make it 0.
"find the numerical value of 2x-3 over x^2-4x+1"
if x=4
2(4)-3 = 8 -3 = 5
4^2 - 4(4) + 1 = 1
5/1 = 5
A. -5x-x over 3-2x B. -x-5 over 2x-3 C. x+5 over 3-2x D. -x-5 over 3-2x
2x^2+7x+3 over x^2-9
2x-3 over 4x^2 - 9
15 ÷ 9x over 10y^3
over
2x^2y^4
(2x+1)(x+3)/(x+3)(x-3) -----> 2x+1/x-3
"2x-3 over 4x^2 - 9"
2x-3/(2x+3)(2x-3) -----> 1/2x+3
"15 ÷ 9x over 10y^3
over
2x^2y^4"
wat