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3-4 DAY 21. A rocket is launching, and its height h in meters is a function of t in seconds (so we are considering the
function h(t)). Explain what h0(10) = 1035 means in language your mom could understand. You answermust include units.
2. Find the derivative of the function.
(a) f(x) = xe1/x
(b) g(x) = tan(2x)1+x
(c) y = (1 + x2)ex secx
(d) h(x) = sin(5x� e�5x)
(e) f(x) =p1 + xe�2x
UAF Calculus 1 1 3-4
Ten Seconds after launch ,the rocket 's height is
increasing at a rate of 1035mA .
- I
= xe×
f ' G) = 1. ex "+× . e×"
. (-1×-2)- I
= ex"
. I'ex
= tanczx ( 1+1,5'
9 'l×7=[seE(⇒ . If ( 1*5 't Ctan2D[ ICHXP. if= 2se.EC#_tan2Xltx
(1+×)2
y '=2x . exsecx + ( HE ) # [e×secx]
= Zxexsecx + ( Hx2)[e×. secx + e× . sealant= e×secx(2× + ( HE )( Htanx ) )
h 'l×7= ws( sx . E.) [ 5 - E5×e5s]
= 5 ( l+I5×)ws(5× - E5×)
= ( 1 +×j2×)"2
fkxttz ( 1+62×512 . ¥ [ ltxet 'T
= IC ltxekjk ( 1. Ext x. eye )
= 'ze2×(1-2×7 ( Hxeexjk
3. Find the equation of the line tangent to the graph of f(x) =p1 + x3 when x = 2.
4. Find y00 for y = 1(1+tan x)2 .
UAF Calculus 1 2 3-4
f (2) = 1+# = 3 's point (2) 3)
f'(x)=lz(1+×3Jk(
3×3=3×22
¥3
3.4 12f
'
(2) =
f=
-6=2line : y
-
3=2(× .2)
y = 2×-4+3
y=@
-2
= ( Htanx )f g
y'= - 2( lttanxpcsecx) = -2 (Htanxfscsecx
'
y't -243Cittaixjt.se#.seEx+CI+tanD3.2CsecxJCsecxtanxD
-# g f g'
= -2 ( -3 seilx ( lttanxjt +2 seixtanx (lttanxp)
= - Zseix
Epa [ 3se5×+ 2tanx( ittanx )]
5. If the equation of motion of a particle is given by
s = A cos(!t+ �)
a particle is said to undergo simple harmonic motion. Find the velocity of the particle at time t and deter-mine when the velocity is zero.
6. The brightness of a star is give by
B(t) = 4.0 + 0.35 sin
✓2⇡t
5.4
◆
where t is measured in days. Find the rate of change of brightness after one day and interpret your answer.
UAF Calculus 1 3 3-4
vats'CA=A[ . sin ( wtts ) . w]
= - Awsm( wtts )
V=o means - Awsm(wt+S)=0zdivide
so sin ( wtts)=oby
- AW
So wtts = Ik.
So t.TK - ST
T
n
BIH - -0.35 . ws(2¥yt) . ftp.fatf
= ( 0.35)ws(E#t) ° }¥,
=2mgi3Iwst¥aA .
B' G) =tf!g;35_)cos(}¥D a 0.1613
After 1 day, the brightenersof the star is increasing
at a rate of
0.1613 pwday .
