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MAC2313C Calculus 3 Summer 2024 Test 2
Name:
Directions: Show all relevant work in the space provided to receive full credit. Give exact answers unless instructed otherwise.
1. (10 points) Let r and u be differentiable vector-valued functions. Prove that
% [r(r) xu(t)] =r(t) x u'(t)- +r/(¢) x u(z)
7 K
2 30 - i“(‘e g h>
—p
m w P
flt <3P' hn, - (\O“P’ hw ), f—n-gm >
e’, = (% bbb ), T gl
/ / /o
a-wp
- Wa
Cqpr
(q7p Wi, - ($pm ), Tm g
_}-<3F-A -(fir)'[«vfl);%‘ 2M>
: N
)
z&i(%, S] k,>+ M<W{§/k> -
4N .,L"J r
S/ S &S S 4
= XM XU
, 2. (10 points) Evaluate
/4
/ [(sec(t)tan(z)i+ tan(r) j + (2sin(z) cos(z)) k)] dt
t=0
2 Smmbmlt) Srmm fam(\ ) (¥ /?>/
2 [ e \"T’i Efinlm(}‘l‘l Lf, 42(t)
-
- l&c“‘ Xeo - ‘ev\ ¢o7,- _}e,‘m)[o)‘\f A. ch[z@.]
— Ak)
MAC2313C Calculus 3 Summer 2024 Test 2
Name:
Directions: Show all relevant work in the space provided to receive full credit. Give exact answers unless instructed otherwise.
1. (10 points) Let r and u be differentiable vector-valued functions. Prove that
% [r(r) xu(t)] =r(t) x u'(t)- +r/(¢) x u(z)
7 K
2 30 - i“(‘e g h>
—p
m w P
flt <3P' hn, - (\O“P’ hw ), f—n-gm >
e’, = (% bbb ), T gl
/ / /o
a-wp
- Wa
Cqpr
(q7p Wi, - ($pm ), Tm g
_}-<3F-A -(fir)'[«vfl);%‘ 2M>
: N
)
z&i(%, S] k,>+ M<W{§/k> -
4N .,L"J r
S/ S &S S 4
= XM XU
, 2. (10 points) Evaluate
/4
/ [(sec(t)tan(z)i+ tan(r) j + (2sin(z) cos(z)) k)] dt
t=0
2 Smmbmlt) Srmm fam(\ ) (¥ /?>/
2 [ e \"T’i Efinlm(}‘l‘l Lf, 42(t)
-
- l&c“‘ Xeo - ‘ev\ ¢o7,- _}e,‘m)[o)‘\f A. ch[z@.]
— Ak)
