Recent content by lude1

Thanks! :)

Homework Statement Find f' of ln[((x2+1).5) / x(2x3-1)2] Homework Equations The Attempt at a Solution I know the derivative of ln(x) is 1/x... however I don't know how to start this particular problem. I think there is a easier way to solve this without trying to solve the...

Homework Statement Evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis. y=(x3/6) + (1/2x), [1,2] Homework Equations 2π∫[r(x)](1+[f'(x)2]) The Attempt at a Solution First I found the derivative. f'(x)= (x2/2) +...

But how would you turn it into a trig substitution problem if the radical is not on the bottom of a fraction?

Homework Statement ∫(1+4x2)1/2 when x runs from 0 to 2. The answer is 4.647 Homework Equations The Attempt at a Solution I tried u substitution, giving me u = 1+4x2 du = 8x where 8 can be pulled out as a constant. But I still have x left over. I'm sure I'm doing something...

Homework Statement The velocity, in ft/sec, of a particle moving along the x-axis is given by the function v(t) = e^t + te^t. What is the average velocity of the particle from time t=0 to time t=3? Answer: 20.086 Homework Equations The Attempt at a Solution Average velocity...

I think why I was confused was, when it said "the rate of change", I instantly thought derivative. When I saw r(t), and not r'(t), I wanted to find r'(t) despite the fact the problem said r(t) WAS the rate of change.

Why would you graph r(t) and not r'(t)?

Homework Statement A pizza, heated to a temperature of 350 degrees Fahrenheit, is taken out of an oven and placed in a 75°F room at time t=0 minutes. The temperature of the pizza is changed at a rate of -110e-0.4t degrees Fahrenheit per minute. TO the nearest degree, what is the temperature...

Homework Statement The rate of change of the altutide of a hot air balloon is given by r(t)= t3 - 4t2 + 6 for 0 ≤ t ≤ 8. Which of the following expressions gives the change in altitude of the balloon during the time the altitude is decreasing? a. ∫r(t)dt when t goes from 1.572 to 3.517...

g''(x)>0 means there must be a place where it is concave up, right? y= 6x-12 is a straight line. y'=6 is also a straight line y'' does not exist? which means there is no concavity which means g''(x) is not greater than 0. Therefore when I plug in 6, I get 24. But because of the conditions...

Homework Statement Let g be a twice differentiable function with g'(x)>0 and g''(x)>0 for all real numbers x, such that g(4)=12 and g(5)=18. Of the following, which is a possible value for g(6)? a. 15 b. 18 c. 21 d. 24 e. 27 Answer: e. 27 Homework Equations The Attempt...

Ooh, okay. I get it now! Thank you so much!

So "the line tangent to the graph of function f" means the derivative. "At the point (1,7) and passes through the point (-2,-2)" means the derivative passes through these two points. Therefore, to find the derivative or the slope, you use the equation y-y1 = m(x-x1). The reason why we know...

Oh, yes, you are right. I forgot that in order for my answer to be right, it had to be (1/2)*∫(2x + 1)1/2du (when x goes from 0 to 2). Thanks!