Post #35

So I need to improve on this thing called calculus.

EXAMPLE 1:
(aSb = integral from a to be)

If aSb f(x)dx=a+2b, then aSb (f(x)+5)dx=

a+2b-(5x)
*have to integrate 5x from a to b)
5b-5a+a+2b
=7b-4a


EXAMPLE 2:

(1/2)Se^(1/2)dt=
u=t/2 du= 1/2dt
1/2Se^u du
2(1/2)Se^u du
e^u +C
e^t/2 +C


EXAMPLE 3:

At what point on the graph of y=(1/2)x^2 is the tangent line parallel to the line 2x-4y=3?

2x-4y=3
formula: -A/B
-2/-4 = 1/2

x=1/2
(1/2)x^2
(1/2)(1/2)^2 = 1/8

(1/2 , 1/8)


EXAMPLE 4:

Let f be a differentiable function such that f(3)=2 and f^1(3)=5. If the tangent line to the graph of f at x=3 is used to find an approximation to a zero of f, that approximation is?

f(3)=2 (3=x, 2=y)
f^1(3)=5 (<--5 slope)

y-2=5(x-3)
y-2=5(3.1-3)
y-2=5(.1)
y=2.5

*It is an approximation so you pick the answer choice closest which is 2.6.


EXAMPLE 5:

If x^2+y^2=25,what is the value of d^2y/dx^2 at the point (4,3)?

x^2+y^2=25
2x+2y(dy/dx)=0
dy/dx= -2x/2y
(2y)(-2)-(-2x)(2dy/dx)/(2y)^2

*plug in point for dy/dx
dy/dx=-2(4)/2(3) = -4/3
2(3)(-2)-(-2(4))(2(-4/3))/2(3)^2
-12-(-8)(-8/3)/2(9)
=-25/27


I need help with:
OPTIMIZATION
ANGLE OF ELEVATION