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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 22
Total: 72
lim
x→
π
2
tan2x
x−
π
2
Solution:  
We have,
lim
x→
π
2
tan2x
x−
π
2
 (0/0 form)
Put x =
π
2
 + y; if x →
π
2
 ⇒ y → 0
lim
y→0
tan2(
π
2
+y)
π
2
+y−
π
2
 =
lim
y→0
tan(π+2y)
y
 = (
lim
x→0
tan2y
2y
) × 2 = 2.
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