Exercise
16.2
Evaluate the following:
1) x
Solution:
x
When x = 0, the given function takes the form
=x
2) x
Solution:
x
When x = 0, the given function takes the form
=x
3) x
Solution:
x
When x = 0, the given function takes the form
=x
4) x
Solution:
x
When x = 0, the given function takes the form
=x
x
5) x
Solution:
x
When x = 0, the given function takes the form
=x
6) x
Solution:
x
When x = a, the given function takes the form
Or, x
= 1.
7) x
Solution:
x
When x = p, the given function takes the form
=x
=x
= (x – p)
8) x
Solution:
x
When x = 0, the given function takes the form
=x
9) x
Solution:
x
When x = 0, the given function takes the form
=x
=
10) x
Solution:
x
When x = 0 , the given function takes the form
=x
11) x
Solution:
x
When x = 0, the given function takes the form
= x
12) x
Solution:
x
=
=
13) x
Solution:
x
= x
= 1.a – 1.b = a – b.
14) x
Solution:
x
= x
= x
15) x
Solution:
x
= x
= x
= x
17) x
Solution:
x
= x
= x
= x
= x
18) x
Solution:
x
= x
= x
= x
= tan
19) x
Solution:
x
= x
= x
= x
= 1 + cot
20) x
Solution:
x
= x
= x
= x
= x
= 1.
21) x
Solution:
= x
= x
= 2 x
22) x
Solution:
x
= x
= x
= –2 x
= –2sin
23) x
Solution:
x
= x
= x
= x
= x
= x
= cotθ + x
= cotθ + x – θ
= cotθ + 1.
24) x
Solution:
x
= x
= x
= x
= x
= cosθ + x
= cosθ + 2θ.sin
25) x
Solution:
x
= x
=
=
26) x
Solution:
= x
= x
= x
= x
= x
= x
= x
= tanθ – x
= tanθ –
27) θ
Solution:
= θ
= θ
= θ
= θ
= θ
=
28) x
Solution:
x
= x
= x
= x
= x
= x
= secc.
29) Find the limit of:
a) x
Solution:
x
= x
b) x
x
= x
c) x
Solution:
x
= x
d)
Solution:
= x
30) Evaluate the limit:
a) x
Solutio:
x
let x – 2 = y → x = y + 2.
So, x → 2 ⇒ y → 0.
Now, = x
b) $ \mathop {\lim }\limits_{x \to \frac{\pi }{2}}
{\rm{ }}\frac{{\cos x}}{{\log (x - \frac{\pi }{2} + 1)}}$
Solution:
= x
Let x – π/2 = y → y ⇒ x =
So, x →
Now,
=x
= y
= –y