Lauren Said:

Can someone please help me out with these AP Calculus questions?

We Answered:

x^2 + 3y^2 = 1 + 3xy..........(1)

a) x=1 ==> 1^2+3y^2=1+3*1*y ==>
y^2=y ==> y^2-y=0 ==> y(y-1)=0 ==> y?=0 and y?=1
There are 2 points: A(1,0) and B(1,1).
First derivative y':
2x+6yy'=3y+3xy'
y'(6y-3x)=3y-2x ==> y'=(3y-2x)/(6y-3x)
1) At the point A: y'=-2/(-3)=2/3
The equation of the tangent line through point A is:
y-0=(2/3)*(x-1) or y=2x/3-2/3
2) At point B: y'=(3-2)/(6-3)=1/3
Tangent line through B: y-1=(1/3)*(x-1) or y=x/3+2/3

b) If the tangent line is vertical, then y'=? ==>
(3y-2x)/(6y-3x)=? ==> 6y-3x=0 ==> x=2y
Substitute x in (1) ==>
(2y)^2+3y^2=1+3*2y*y ==>
y^2=1 ==> y=-1 (x=-2) or y=1 (x=2)==>
The tangent lines are vertical at the points (-2,-1) and (2,1).
Their equations are x=-2 and x=2 respectively.

Dustin Said:

Calculus Ap questions 1976?

We Answered:

Substitute the equation into the definition of a derivative.

1. lim(h-->0)((x+h)^2+(x+h)-(x^2+x))/h
expand: lim(h-->0)(x^2+2xh+h^2+x+h-x^2-x)/h
simplify: lim(h-->0)(2x+h+1)
apply the limits: 2x+1

2. lim(h-->0)(cos(x+h)-cosx)/h
expand using trig identidy:
lim(h-->0)(cosxcosh-sinxsinh-cosx)/h
rearrange: lim(h-->0)(cosx(cosh-1)/h)-(sinxsinh/h)
use the trig identities:
lim(h-->0)(cosh-1/h)=0
lim(h-->0)(sinh/h)=1
answer: -sinx

Julie Said:

are you allowed to omit questions on the ap calculus bc exam?

We Answered:

Yes, you can omit them just like the SAT. Statistically speaking, I would say that you shouldn't omit more than one out of every four questions if you want to get a 4, although it really depends on how the people taking it with you fair on the questions that you omit.

Good luck!

Lonnie Said:

AP calc questions, where can i find them?

We Answered:

Try the College Board's website at www.collegeboard.com. Try searching "AP Calculus free response" in Google or something. Also, consider investing in a test prep book.

Allen Said:

can u omit questions on the ap calculus bc exam?

We Answered:

You can omit MC questions on on all AP Exams. There a total of 45 questions on the calculus bc exam, so i would try to omit no more than 8-10....