Find the Derivative
6x3+2x2-6
18x2+4x
x4
(x5/5)+C
A particles position is at x=3. The particles velocity is greater than zero. Is the partical moving closer or farther from the origin?
Farther
as x approaches 3
-1/10
What does EVT stand for?
Extreme Value Theorum
F(x)= 3x2
G(x)= 1/x
(d/dx) F(x)*G(x)=?
3
(2/3)x8+x(3/2)
(2x(5/2)/5)+(2x9/27)+C
A particles has a positive position, a positive velocity, and a negative acceleration at a certain point, R. Is the particle speeding up or slowing down at R?
Slowing down.
lim (x2+500)/(x2+1000)
as x approaches infinity
1
What does MVT state?
A continuous and differentiable function has a point where the instantaneous rate of change equals the average rate of change
OR
f1(x)=(f(b)-f(a))/(b-a)
F(x)= x5+6(x-1)
G(x)=e2x
(d/dx) F(x)/G(x)
e-2x(-2x5+5x4-12x+18)
4/x2
4/x + C
A particles has a maximum velocity at X=4. What can be assumed about acceleration at X=4?
A) a(4)<0
B) a(4)=0
C a(4)>0
B
lim (x4-5x+200)/(x2+1000x+1000)
as x approaches 0
1/5
What is the Fundemental Theorem of Calculus for definite integrals?
integral from a to b of f(x)dx = F(b)-F(a)
Sin(5x/4)
5/4(cos(5x/4))
5x-3
5x-2/2 + C
A particle has a positive velocity at X=4. What can be assumed about position at X=4?
A) p(4) is increasing
B) p(4)= 0
C) p(4) is decreasing
A
lim (x1/2-2)/(x-4)
as x approaches 4
1/4
What does L'Hospital prove?
If lim x->a of f(x)/g(x) is undefined or infinity/infinity,
then the limit of f1(x)/g1(x) as x-> a is equal to the limit of f(x)/g(x) as x-> a
ex^3+x^(1/2)+4
(ex^3+x^(1/2)+4)(3x2+(1/2x(1/2)))
3x2sinx
3x2cosx + 6xsinx + 6cosx + C
Is a particle's position is defined as p(x)= 4x3+6x+23, what is an equation for the particle's acceleration? What is a(1)?
a(x)=24x
a(1)=24
Evaluate the limits and determine if it exists or not.
lim (10+|x-5|) as x approaches 5
10
limit exists
What is required to complete an indefinite integral?
+C