Extra credit problem for calculus?
2. Researchers at Iowa State University and the University of Arkansas have developed a piecewise function that can be used to estimate the body weight (in grams) of a male broiler during the first 56 days of life:  where t is the age of the chicken (in days). a. Determine the weight of a male broiler that is 25 days old. b. Is W(t) a continuous function? Explain why or why not.
Calculus II Question. Euler also found the sum of the p-series with p=4?
a) Σ(n = 1 to ∞) (3/n)^4 = Σ(n = 1 to ∞) 81/n^4 = 81 Σ(n = 1 to ∞) 1/n^4 = 81 * π^4/90 = 9π^4/10. b) Σ(k = 5 to ∞) 1/(k-2)^4 = 1/3^4 + 1/4^4 + 1/5^4 + ... = (1 + 1/2^4 + 1/3^4 + ...) - (1 + 1/2^4) = π^4/90 - (1 + 1/16) = π^4/90 - 17/16. I hope this helps!
Calculus in Skiing? Calculus Extra Credit?
What forces are used to execute ski jumps ?
Calculus II Questions, or an online Calculus calculator?
1) Let y1=-3x+6 and y2=x²-4, y1 and y2 intersect at y1=y2 ==> -3x+6=x²-4, x²+3x-10=0 ==> x1=-5 and x2=2 y1>y2 for any x in the interval (-5, 2) ==> Area=∫[-5, 2] (y1-y2) dx = ∫[-5,2] [-3x+6-(x²-4)] dx = ∫[-5,2] (-x²-3x+10) dx = -x³/3-3x²/2+10x [x=-5 to 2]= -8/3-6+20-(125/3-75/2-50)=57 1/6 2) V=π∫[-1,1] y² dx = π∫[-1,1] sqrt(x+1)² dx = π∫[-1,1] (x+1) dx = π∫[-1,1] (x+1) d(x+1) = π(x+1)²/2 [x=-1 to 1]=2π or V=π∫[-1,1] (x+1) dx = π(x²/2+x) [x=-1 to 1]= π[1²/2+1-(-1)²/2-(-1)]=2π 3) http://i299.photobucket.com/albums/mm286... Let y1=x², y2=1 and y3=-2 y1=x² and y2=1 intersect at y1=y2 ==> x²=1 ==> x1=1 and x2=-1 V=π∫[0,1] [(y2-y3)²-(y1-y3)²] dx = π∫[0,1] [(1+2)²-(x²+2)²] dx = π∫[0,1] (9-x⁴-4x²-4) dx = π∫[0,1] (5-x⁴-4x²) dx = π(5x-x⁵/5-4x³/3) [x=0 to 1] = π(5-1/5-4/3) = π * 3 ⁷/₁₅
Why did my Calculus 2 professor give me an impossible question?
*A2AYou’re right that the denominator is simply the sequence [math](n+1)[/math]The numerator is the sequence [math]n^2[/math]They change signs for every consecutive term…Introduce a [math](-1)^n[/math], so that it will take care of the alternating signs.Notice that you have to start from [math]n=1[/math], which will make [math](-1)^1=-1[/math], which means the first term will become negative. We don’t want that, so let’s fix it.Write the alternating sign generator as [math](-1)^{n+1}[/math]Put everything discussed so far together as a sequence.You should have the following generator….[math](a_n)=(-1)^{n+1}\dfrac{n^2}{n+1}\tag*{}[/math]Updating my answer due to the posted comment.Regarding the sum of the series (if the sum of the sequence is taken)[math]S=(-1)^{n+1}\dfrac{n^2}{n+1}\tag*{}[/math]Consider the sequence [math]b_n=\dfrac{n^2}{n+1}[/math]It’s easily seen that the sequence is monotonic increasingThe limit [math]\lim_\limits{n\to\infty} b_n=\infty[/math]Hence the sum to infinity of this series diverges via the Alternating Series Test
Calculus - Testing for Convergence using the Integral Test?
webwork was due yesterday.. are you in 160A and math 5c??
Math Calculus help! i need the extra credit please! 30 points!?
I am not sure if this answer will be in the form required but it may help you.. D = 0.01t^2+.5t Differentiate to get rate of change.. dD/dt = 0.02t + 0.5 Rate of movement cm/day (note it is linear) dD/dt = 0.02*40 + 0.5 = 1.300 cm/day when t= 40 dD/dt = 0.02*40.1 + 0.5 = 1.302 cm/day when t= 40.1 Average over period (1.300+ 1.302)/2 = 1.301 cm/day Expression for average rate of change from 40 to 40+w days (I will not use symbol t to save confusion) dD/dt = 1.300 when t = 40 (w = 0) dD/dt = 0.02(40+w) + 0.5 at any time 40+w dD/dt = 0.8+0.5 + 0.02w dD/dt = 1.300 + 0.02w So average at any time t (after 40 is) = (1.300 + 1.300 + 0.02w)/2 cm/day = 1.300 + 0.01w cm/day w may be viewed as dt ? Limit as t approaches 40 In other words as w approaches zero Will obviously be 1.300 cm/day
How important is Calculus 2 for Engineering?
I’d like to give an expanded answer here: Things like Taylor’s formula and power series aren’t really the “engineering” things that will carry over. Sure, you’ll probably run into series again in Thermodynamics, but they will be a more simplified version in the sense that you’ll likely be told that the series converges and to what it converges.The big things you’ll need are the integration techniques. A lot of problems in engineering are differential equations, which you need a slew of integration techniques to solve. Things like integration by parts, trig substitution, change of variable, and so on. As you progress onward, you’ll see more and more of them pop up.I would recommend taking Calculus II again in college. It’s going to be much more detailed than your high school class is, and give you a much smoother transition into differential equations. I’d also recommend taking Calculus III and Linear Algebra before Differential Equations. If you get a good handle on Calculus and Linear Algebra, Differential Equations will be a cake walk, and you’ll look like a pro compared to your fellow classmates.