# Search results

1. ### Substitution with integration

i finally found my error. I understand the basics(for the most part) of integration. It is the substitution and the more sophisticated equations that get me.
2. ### Substitution with integration

I cannot believe this, same problem but it is /int 4_0. I'm sorry i missed that. To answer the question of what i am doing, first I have to figure out if this is something i can use the fund. rules of integrals or something i have to (or is preferred) substitute the function. For this one, i...
3. ### Substitution with integration

I did this: u^(1/2)/(1/2). 2u^(1/2) 2(2t+4)^(1/2) (4t+8)^1/2 (12t)^(1/2) 2(3)^(1/2) I believe I am further off than the first time.
4. ### Substitution with integration

Homework Statement /int (2t+4)^-1/2 dt. the answer is 2(sqrt3)-2 Homework Equations The Attempt at a Solution u^-1/2*(1/2)du (-1/2)(u^1/2) (-1/4)(2t+4)^1/2 (-1/4)(sqrt 12)= (-1/4)(4(sqrt 3)/1)=sqrt 3 (sqrt 3)-1/2 2(sqrt 3)-1
5. ### Definite integration 2 & 3

I found what i did wrong now. thanx
6. ### Definite integration 2 & 3

Homework Statement 2. /int 1_0 (5u^7+pi^2) dx the answer is (5/8)+pi^2 3./int 4_0 (x^(1/2))(x+1) the answer is 272/15. Homework Equations The Attempt at a Solution For 2. I already have the 5/8, my question do I integrate the pi^2? I tried integrating that with no success. For...
7. ### Definite integration

ok i got it now. thanx
8. ### Definite integration

that was pretty much it. did u put x^3 on top? or did you left the x^3 on the bottom? Because i believe that was my problem on this one.
9. ### Definite integration

My apologies, it is 2_1 not 9_0
10. ### Definite integration

Homework Statement integration 9_0 c/x^3 dx. the answer is (3/8)c. Homework Equations just distrib. then plug in the #'s The Attempt at a Solution =cx^-3 = (cx^-2)/-2=c/-2x^2 I know it has something to do with distribution.
11. ### Reverse diferentiation problem

Now I know what I did wrong now, I just put x^-4 on top instead of subtracting the lower from the upper which I should have done. Thanks glenn
12. ### Reverse diferentiation problem

Homework Statement (x^2+3x-1)/x^4 the answer is,(-x^-1)-(3/2)(x^-2)+(1/3)(x^-3)+C Homework Equations Just reverse diferentiation The Attempt at a Solution =x^2+3x-1+x^-4 =(x^3)/(3)+(3x^2)/(2)-x+(1/3)(x^-3+C) (1/3)(x^3)+(3/2)(x^2)-x+(1/3)(x^-3)+C I know i got the answer but somehow it is...
13. ### L'hopital's rule

I now get the infin. multiplication part now. also, f'(x)=ln(x) g'(x)=x^5 was meant to be: f'(x)=ln(x) ----------- g'(x)=x^5 Thanks
14. ### L'hopital's rule

For 1. I would have to apply l'hopital's again because it is still 0/0. So, it would be(2-2cos(2x))/(4xcos2x+2sin2x). It is still 0/0 so i have to derive one more time. It would be 4sin2x/4xcos2x+4cos2x. Apply the 0 and got 0/4 = 0. Did I do this right now? 2. a. The limit of ln(x) is -infin...
15. ### L'hopital's rule

I would like to know if I did these the correct way. Homework Statement 1.lim x->0 (1/sin 2x)-1/2x. the answer is 0. 2.lim x->0 (x^-5*ln x). The answer is -infinity. Homework Equations 1.I used L'Hopitals theorem 2.I derived them, than L'hopitals. The Attempt at a Solution 1.I...
16. ### Huge problem with relation rates.

Homework Statement I search all over my textbook and did not show any (simple) examples on relation rates(seriously). Well, The first problem is, x^2+y^2=25 find dy/dt when x=3. dx/dt =4 and it says find the indicated rate and assume x>0 and y>0 Homework Equations I did my best...
17. ### Implicit differentiation

I don't know if I got this right. I used the product rule: (x)(y(x))'+(x)'(y(x)) and for derivitive of y(x), I used the chain rule to find the derivitive. And got(x)(1*x*x)+(x)(y(x)). -> x^3+xy(x)d/dx=0 What else am I doing wrong?
18. ### Implicit differentiation

Homework Statement I just got started on this, and am not grasping the WHOLE idea. 1.xy=25 The answer says -y/x 2.x^2+3xy+y^2=15 And this says -y^2/x^2 Homework Equations 1. dy/dx(xy)= dy/dx(25) 1=0 ??? 2.dy/dx x^2+3xy+y^2= dy/dx 15 2x+3+y(dy/dx) =0...
19. ### Finding the equation for the tangent line.

For this problem, Yes
20. ### Finding the equation for the tangent line.

I saw my mistake, I did the derivative wrong. sorry
21. ### Finding the equation for the tangent line.

Homework Statement find the equation for the tangent line. 1. (e^x)(cos x) where x=0 Homework Equations plugged 0 into the equation, (e^0)(cos 0) and got 1 for the y-coordinate. so I got the points(0,1). For the slope, I derived the equation into -(e^x)(sin x). then i plugged 0 in and got 0...
22. ### Derivitives of Trig.

I think I get what u 2 are saying... since sec^2-tan^2 equals 1, it would be 1+cosx, take the derivative and I get -sinx?
23. ### Derivitives of Trig.

3. sinx^2/cosx^2 (cosx^2)(sinx^2)'-(cosx^2)'(sinx^2) ------------------------------------ (cosx^2)^2 (cosx^2)(2 cos x sin x)+(2 cos x sin x)(sinx^2) ---------------------------------------------- (cosx^2)^2 (2 cosx^2*cosx^3*sin x cosx^2)+(2sinx^2*cosx sinx^2*sinx^2)...
24. ### Derivitives of Trig.

For 1, I am really not seeing how it becomes sin2t from 2sinx cosx. For 2, I got it right, it was the derivative of e^2x that messed me up. thanks cristo. For 3, I know ultimately the third term will be left and the other two will cancel each other out. This is what i got(by following the...
25. ### Derivitives of Trig.

For 1. I tried the chain rule(sin x inside, square outside), and it got me 2cos(t) which is worse than my first answer. For 2. I assumed e never changes. And I never came across a problem where e changes and I am not too sure on how to do that. Is it 2 e^1? For 3. If I am understanding this...
26. ### Derivitives of Trig.

Homework Statement 1. Sin^2(t) The answer states sin2t 2. (e^2x)(sin x-cos x) The answer states (e^2x)(3 sin x- cos x) 3. sec^2(x)-tan^2(x)+cos(x) The answer states -sin x Homework Equations 1.product rule 2.product rule 3. sum and diff. rule? The Attempt at a Solution 1. (sin...
27. ### Derivitive problems

Thank you, I will keep that in mind.
28. ### Derivitive problems

actually that is what I was trying to say, didn't know how to write it. now I am aware the h cancels, for it to be, 5/(sqrt 5x+5h +sqrt5x). I know I cannot add (sqrt 5x+5h +sqrt5x) together because it is not like. If I am wrong about that, let me know. Am I suppose to distribute it back? I don't...
29. ### Derivitive problems

i multiplied the rad. on the numerator by (sqrt 5x + sqrt 5h) +(sqrt 5x) (since numerator has negative sign), and i got 5x+5h-5x/h(sqrt 5x + sqrt 5h) +(sqrt 5x). both 5x's on numerator go for it to be 5h/h(sqrt 5x + sqrt 5h) +(sqrt 5x). I'm not sure on how to get (sqrt5x)-2x from...
30. ### Derivitive problems

Homework Statement The directions state, Use the definition to differentiate the functions given. 1)f(x)=sqrt 5x. the answer states: (square root 5x)/2x. The directions state, a. Find the difference quotient of f. and b. f'(c) by comparing the limit of the difference quotient. Also, c is a...