(c)
f(x) = 
(d) f(x)
= |x ? 5|
continuous
at x = 0? At x = 1?
a
continuous function ?
is
continuous at x = 3.
is
the function
continuous
at x = 0?
What
about continuity at x = 1?
?
is
a continuous function.
at
x = 2.
at x = 
at x = 5.
is
a continuous function.
Is not differentiable at x = 1*
find 
0 < x
< 1, find 
.
0 <
x < 
], find 
.
find 
w.r.t.
x.
w.r.t. x.
in two
ways- Ist by repeated application of product rule and second by logarithmic
differentialtion.
y = b cos find 
.
find 
find
and
y = 
? sin 
find 
(1
+ cos 
), find 
.
find 
), y = a sin
t, find 
+ sin ), and y =
a (sin ? cos ), find 
show that 
in terms
of y alone.
is
differentiable functions and if f?(x) does not vanish any where, then prove
that f(?5) 
f(5).
for which
f?(c) = 0
for
x > 3.
if y = sin?1
x + 
.
for |x|
< 1, prove that
is a constant
and independent of a and b.
Prove
that
Prove that 
II. f(x) = sin
x + cos x, 
III. f(x) = 4x
IV. f(x) = (x ? 1)2
+ 3x 
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