Homework Statement
the maclaurin series for f(x) is given by 1/2! - x2/4! + x4/6! - x6/8! + ... + (-1)nx2n/(2n+2)! + ...
a) Let g'(x) = 1-x2 * f(x)
Write the Maclaurin series for g'(x), showing the first three nonzero terms and the general term.
b) write g'(x) in terms of a familiar...
Homework Statement
The graph of the polar curve r=2-cosΘ for 0≤θ≤2pi is shown in the figure. (attached)
a) write an integral expression for the area of the region inside the curve
b) write expressions for dx/dΘ and dy/dΘ in terms of Θ
c) find dy/dx as a function of Θ
d) write an equation in...
Homework Statement
if the series ∑(n=1, goes to infinity) (-1)^n/(n^3)
is approximated by its ninth partial sum, find a bound for truncation error
Homework Equations
Alternating Series Estimation Thm:
If alternating series is CONVERGENT, then truncation error for nth partial sum is less than...
Homework Statement
A partcile starts att he point (1,0) and t=0 and moves along the x-axis so that at time t≥0 its velocity v(t) is given by v(t)= \frac{1+ t}{(1+t^2)}
A) Determine the maximum velocity of the particle.
B) Find an expression for the position s(t) of the particle at time t...
ok, I see. So i took dw/dt = kw and got
∫1/w dw = ∫k dt
lnw = kt + C
Using (0,2) to find C:
ln2 = C
Using (4, 3.5) to find k:
ln3.5 = 4.5k + ln2
4.5k = ln(1.75)
k=1.124
So, lnw= 0.124t + ln2
w=2e^(0.124t)
to plug in 6 months:
w(6)= 4.218
How come I didnt get the correct...
Homework Statement
Suppose that during the first year after its hatching, the weight of a duck increases at a rate proportional to its weight. The duck weighed 2 pounds when hatched, and 3.5 lbs at age 4 months. How many lbs will it weight at 6 months?
A) 4.2 lbs
B) 4.6 lbs
C) 4.8 lbs
D)...
Homework Statement
The line x-2y+9=0 is tangent to the graph of y=f(x) at (3,6) and is also parallel to the line through (1,f(1)) and (5,f(5)). If f is differentiable on the closed interval [1,5] and f(1)=2, find f(5)
A) 2
B) 3
C) 4
D) 5
E) None of these
The correct answer is (C) 4The Attempt...
Homework Statement
An equilateral triangle with side length x sits atop a rectangle with a base length of x, with the base of the triangle coinciding with the top base of the rectangle. the height of the rectangle is 7 times the length of its base. If the combined area of the figures is...
Question:
Particle A is resting on the origin. Particle B travels along the path of f(x)=-cos(x-7)+3. What is the minimum distance that the particles can be apart?
Attempt:
I tried to find the minimum of f(x)=-cos(x-7)+3. So I found when the derivative is 0:
dy/dx= sin(x-7)...
Homework Statement
A represents the 1st quadrant area bounded by f(x)=e^(-tanx), y=.01, y=.09, and the y-axis. Write an integral expression for the volume of the figure that results from revolving A around the line x=30.
Homework Equations
The Attempt at a Solution
So, I know that I have to...
How do you find average acceleration given a table with points of velocity (ft/sec)?
t (sec): 0 15 30 45 60
v(t) (ft/sec):0 40 60 70 75
the question asks: Find the average acceleration of Rocket A over t=[0,60] seconds.
I used change in v(t)/change in time to find 4...