UPSEE Solved Model Paper 1

lim

x→0

ae−x−bcosx− 1 2 cx

xcosx

= 2
At x = 0, denominator = 0, Numerator = a - b
For limit to be exist numerator should also be = 0
So,
a - b = 0 ⇒ a = b ...(i)
Now Apply L' Hospital rule

lim

x→0

ae−x−bcosx− 1 2 cx

xcosx

=

lim

x→0

[ d dx (ae−x−bcosx− 1 2 cx)]

d dx (xcosx)

=

lim

x→0

−ae−x+bsinx− 1 2 c

−xsinx+cosx

= - a -

1

2

c
⇒ - a -

1

2

c = 2
𝑐 = −2𝑎 − 4
𝑎 + 𝑏 + 𝑐 = 𝑎 + 𝑎 + (−2𝑎 − 4)
= −4