Question

Q.4 Find the value of limx → 0⁡(Sin(2x))Tan2 (2x)? *

a) e0.5

b) e-0.5

c) e-1

d) e​

Answer 1

Answer:

lim

x→0

x

3

tan2x−sin2x

=lim

x→0

⎝

⎜

⎜

⎛

x

3

cos2x

sin2x

−sin2x

⎠

⎟

⎟

⎞

=lim

x→0

sin2x

⎝

⎜

⎜

⎛

x

3

cos2x

1

−1

⎠

⎟

⎟

⎞

=lim

x→0

x

3

sin2x

(

cos2x

1−cos2x

)

=lim

x→0

x

3

sin2x

(

cos2x

2sin

2

x

)

=lim

x→0

2

1

×2x

sin2x

×

x

2

2sin

2

x

×

cos2x

1

using multiple angle formula cos2x=1−2sin

2

x

=lim

x→0

2(

2x

sin2x

)×2

x

2

sin

2

x

×

cos2x

1

by rearranging the terms

=2×1×2×1×

cos0

1

since lim

θ→0

θ

sinθ

=1

=4 since cos0=1