NCERT Class XI Mathematics - Limits and Derivatives - Solutions
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Question : 37
Total: 72
For the function
f (x) =
+
Prove that f ′(1) = 100 f ′(0).
f (x) =
Prove that f ′(1) = 100 f ′(0).
Solution:
We have
f (x) =
+
Differentiating (i) with respect to x we get
f' (x) =
+
⇒ f' (x) =1 99 + 1 98
At x = 1
f' (1) =1 99 + 1 98
and f' (0) = 0 + 0 + ... + 0 + 1 = 1
Hence f ′(1) = 100 f ′(0).
f (x) =
Differentiating (i) with respect to x we get
f' (x) =
⇒ f' (x) =
At x = 1
f' (1) =
and f' (0) = 0 + 0 + ... + 0 + 1 = 1
Hence f ′(1) = 100 f ′(0).
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