# Search results

1. ### 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
2. ### 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...
3. ### 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.
4. ### 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...
5. ### 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...
6. ### 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...
7. ### 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...
8. ### 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...
9. ### 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...
10. ### 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...