Mathematics Times – July 2019

f0 0 and f0 0

When x y0, 0

y is continuous at x0.

Clearly at all other points y is continuous. Therefore,

the set of all points where fog is discontinuous is

an empty set.

22.Sol: Given, the curves

2 2

1

4

x y



  and y^3 ^16 x

intersect at right angle.

i.e., product of slopes of their tangents is equal to

 1.

Now, m 1 is in the slope of tangent of the curve

2 2

1

4

x y



 

i.e.,^1

4

2

x

m

y





and^22

16

3

m x

y



2

4 16

1

2 3

x

y y



   

i.e., 3 y^3  64 x

64 4

3 16 3

x

x

  



23.Sol: Given x a sin^1 t

22.Sol:

23.Sol:

2 1^2

log

dt t

dx x a

  

(1)

and

cos^1 t

y a





2 1^2 log

dy y

a

dt t



 



(2)

from (1) and (2) , we get

dy y

dx x



(^22)
(^112)
dy y
dx x
    
  
2 2
2
x y
x
 