Download Ap calculus questions and more Exercises Mathematics in PDF only on Docsity!
AP Calculus
,?"'\ SHOW ALL WORK Ill
Find dy/dx as a function of x.
- y=(-2x+l0) 3
'f'-:. l3l(-2')(t(0)1. (-).,
'/-:. _ b (-1.l)(tlO)'
Chain Rule WS
Find the derivative of the function. "t
- :l1£ {'-('t-) !.
{)~ -'t, : , ({5 f :fl r2. r I 5- cJ , 1•
~': i ( /5,-~1r;:- [ 15-~o)
Name 511\wi.w....J
Bloc k:
Finddy/dt.
- y=t5(t^4 +8)^5
y' .Q 1 (r'tg)5, (~(t 'tstf ) (t ')
. £i-t
- (xLsr5 y':. -5(xt..sf\f,x-f}
y''= (y! b)-('=tr-~t ({r1] (-/~sr-t~ -i)_
t. --b(1Ls}. if¾
ll) y= 3 x5 (4x -6 )2 N1-6)(2fx 5 ) ' ;
V ':: {4x-6f(l5,x'f}1 (3?< 5 ) · J('f,:-6)(qT
y ,, : (1x-6r ( /20,x)}-t l/5'X'f)- 2(~ix-b) (4) + (~x-b )
( n,Ory<1) -t (21./xs/ ('i)
Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values of x. Find the derivative with respect to x of the
given combination at the given value of x.
x f(x) (x) { (x) ' (x)
- 3 1 16 6 7 4 -3 3 5 -
f(g{x)), X = 4-
f !~I~)}· ~'fa)
:r'(,) '-b
.,__ b. - h
: -~b x f(x) (x) { (x) (x)
- 3 1 9 8 5 4 -3 3 5 -
~ , x= 3 [rjlx)}
1
{ (~rx) ri (~I [x))
- ½( 9 f½ f')
x f(x) (x) { (x) (x)
- 3 1 16 6 5 4 3 3 5 -
x=3 i (fM-t~/11)) (f(~ (,'~\
i (1,16J{6,t5)
: 3.(11)111)
Solve the problem.
- The position of a particle moving along.a coordinate line is s=~ withs in -- meters and tin seconds. Find the particle's velocity at t = 1 sec. s : (q t\1-t)
II: ½:l'Hl'l)(11.) 6('/fllt)
I
)h, v-il')
- The position of a particle moving along a coordinate line is s =~with s in meters and t in seconds. Find the particle's .i.
acceleration att:;c 11 sec. S : 'o tb{) 2.
II'- t{3-lb{J•(b) = -
">: - ½.(3tbdt6Jl:i,} -:.{?>+bt)-q)
,._(f}:,~ \
-rtr~ :_ 2+
Find a and b so that f is continuous at every point.
J§2..
x^2 , x<- f(x)= ax+b,-5:!:ix:!:i - x+6, x>-
- -----2.^ Find^ th^ e^ limi^ t.
x f(x ) {x) ( (x) (x)
- 3 1 4 6 7 4 -3 3 5 - I
g(x +f(x)), x = 3 ~, { i+ f (x}) {~-tf !1)
:~ '{ 3t l) (l +b )
" -5 • l-
2
- Jim -^ 14x2-^ 3x^ +1^7 x-+-"' -6x^2 +Bx + 13
