chapter 6
solve the differential equation
dy/dx=Y+5
e^(x+c)-5
or Ce^x -5
find the area of the region bounded by the graphs of the following equations:
y=(x^2)-5x+2
y=-2(x^2)+5x+2
18.5185
integral of (a^u)du
(1/ln(a))a^u +c
what does monotonic mean?
it means a function is either always increasing or decreasing.
given r=6, find the area in first quadrant
7.069
solve the differential equation
2dy/dx-3xy=0
e^(3/4x^2)+c
or Ce^(3/4x^2)
find the volume of the solid bounded by:
y=x+4
y=(x^2)+2
revolved about the x-axis
101.787
integral of (-(4x^2)cos(3x)
-4/3x^2sin(3x)- 8/9xcos(3x)+ 8/27sin(3x) +C
find whether infinity E n=0 of (1/n+1)^3/2 converges or diverges? give justifacation
converges by direct comparison
find the total distance traveled of a particle defined by the parametric equation
dx/dt=3cos(e), dy/dt= 5t^2 +1
from t=0 to t=4
112.073
given f(1)=5 and dy/dx=(x^2)+4, approximate f(2.2) using eulers method using a step size of h=.4
12.28
find the volume of the solid bounded by:
x=0 y=2x+4
y=0 x=3
revolving about the x axis
490.08
lim as x->0+ of (xe^5x)/(2x^3)
undefined
how many terms for infinity E n=1 of (-1)^n/n^3 would the error remainder be less than or equal to .001.
n=10 by alternating series remainder theorem
find where d^2y/dx^2 is undefined on [0,2pie]
dx/do=-6cos(o)
dy/do=-4sin(o)
o is theta
undefined at pie/2 and 3pie/2
what are the three requirements of the domain of a particular solution
1. must satisfy the domain of the particular solution
2. must satisfy the domain of the original solution
3. must be the largest single interval that contains the given point.
find the area of the region bounded between f(x)=cos(x) and g(x)=(x+1)^2 -5
15.882
what are the steps for decomposing p(x)/q(x) into partial fractions
hint: 4 steps
1. if degree of p(x) is greater than the degree of q(x), divide
2. factor denominator completely
3. breakdown into linear fractions
4. break down quadratic functions
what are the three requirements of integral test of f(x)
1. always positive
2. f(x) is always continuous
3. f(x) is decreasing
given x=4t^3-9cos(t) and y=5t+12t^2, find the arc length from 1 to 4
329.339
solve the particular solution of dy/dx=3(x^2)y-y satisfying (1,3)
find the volume when the region is bounded by:
x=0 x=3
y=x^3+4 y=1
revolved about the y-axis
does not need to be simplified
integral of (-9x+8)/(x^2-3x)
-8/3ln(x)-19/3ln(x-3)+c
parenthesis are absolute value lines
https://drive.google.com/file/d/1HYWh_wJWLaczPI8GhHvDGQSs7wqNvA3P/view?usp=sharing
write the first three non-zero terms of the maclaurin series for e^(3x)^2 along with the general term
1+9x^2 + 27/2x^4 +...+ (3x)^2n/(n!)
https://drive.google.com/file/d/1P8ZpkEYvPzdAQzCaKzJ0uWTh411OrGQf/view?usp=sharing
find the slope of the polar equation defined by r=4+sin(o) at pie/3.
o is theta