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Calculus Exam 2017 model
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Model Answer
Answer the following questions 20 questions
Q(1) If F(X ) =
c e
X , then F /// (3 ) equals……………..…… X−2
d f
-36 6
-12 4
/ // /// F (X ) = X − 2 − 2X = −2(X − 2)−2 ∴ F (X ) = 4(X − 2)− 3 ∴ F (X ) = −12(X − 2)− 4 = −12 (X − 2 )
Q(2) If
c e
(
)
2
F(X ) = ln X2 + 1 + e sin X
then F / (0 ) = .. ……
d f
1+e e
1 0
/ sin X / sin 0 F (X ) = 42 X + cos Xe ∴ F (0 ) = 42× 0 + cos 0 × e =1 X +1 0 +1
Q(3) If F(X ) = X X then F / (1) = ………….…….
c e
e -1
Y = X
X
∴ lnY = XlnX
/
∴ Y = ln X + 1 Y
d f
1
/
X
0
∴ Y = X lnX + X
X
= 1
Q(4) A body moves on the curve Y 2 = X 3 If dX = 1 unit / sec when Y=-1 then dY at this moment equals…….. dt
c e 2Y
− 3 4 3 4 dY dX = 3X 2 dt dt
dt
2
unit/s
d f Y = -1∴ X = 1 ∴ 2(- 1) ×
− 3 8 3 2
dY dY 1 3 = 3(1)2 × ∴ =− dt dt 2 4