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Q.4 Find the value of limx → 0(Sin(2x))Tan2 (2x)? *a) e0.5b) e-0.5c) e-1d) e |
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Answer» Answer: lim x→0
x
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 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 |
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