MA 3972-MA-Book April 11, 2018 16:20400 STEP 5. Build Your Test-Taking Confidence
ln|y|=∫
1
2x−^2 dx=1
2
(x−^1 )
− 1+C
=−
1
2 x+C
eln|y|=e(−
21 x+C)
y=e−
21 x+C
; f(2)= 1
1 =e−
2(2)^1 +C
⇒ 1 =e−(^14) +C
Sincee^0 =1, −
1
4
+C= 0 ⇒C=
1
4
.
Thus, y=e−
21 x+^14
.(D) f(2.5)=e(−2(2^1 .5)+^14 )
=e(−(^15) + (^14) )
=e
201