Question

Show that the function defined by f(x) = sinx^2 is a continuous function.​

Answer 1

Answer:

Let p(x)=sinx;9(x)=x ^2  [x∈R]

Both p(x) and q(x) are always continuous.

So, p(q(x)) is always continuous

So, sin(x^2) is a continuous function.

Answer 2

Given :  f(x) = sinx²

To Find : Show that function is continuous

Solution:

f(x) = sinx²

f(t)  =sin t

where t  = x²

f(x) = sin x  is a continuous function  for  x ∈ r

t = x²

t ∈ ( 0 , ∞)  for x ∈ R

Hence f(t) = sin t   is continuous   as  t  ∈   ( 0 , ∞)  ⊂ x ∈   R

Hence

f(x) = sinx²  is continuous function

Learn More:

3) Fidelity records the number of X-Trails sold each day. This data is ...

brainly.in/question/21911816

the following distribution gives the cumulative frequency of more ...

brainly.in/question/7290782