CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 13 – Limits and Derivatives Maths
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f '
x
lim
h0
lim
h0
h0
x h 1 x h 2x 1 x 2
2 2 2
x hx 2x hx h 2h x h 2x 2x x 2
f x h f x
lim
h0
h
2
hx hx h 2h h
lim
h0
h
2
2hx h 3h
lim
h0
h
lim 2x h3
h
2x
3
1
(iii) Let f(x) = . Accordingly, from the first principle,
2
x
f x h
f x
f ' x
lim
h0
h
1 1
2
2
x
h
x
lim
h0
h
2
2
1 x x h
lim
h
0
2 2
h
x x h
2
2
1 x x h
lim
h
0
2 2
h
x x h
2 2 2
1x x h 2hx
lim
h
0
2 2
h
x x h
2
1h 2hx
lim
h
0
2 2
h x x h
2
h 2x
lim
h
0
2 2
x x h
02x
2
2
x x0
x
2 3
(iv) Let f(x) =
h
x1
. Accordingly, from the first principle,
x 1
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