rate of change

**Angel Rox** · December 11th 2008, 07:19 PM

Q1- The distance traveled by an object at time t ≥ 0 is s = f(t) = t^2 where s is in meter (m) and t in seconds (sec). Find the instantaneous velocity of the object at t = 2sec

Q2- Find the natural domain of the given function

h(x) = 1/1-sinx

Q3- What are the points of discontinuity for the function f(x)=x+5/x^2-1 ?

**Erdos32212** · December 11th 2008, 07:34 PM

Originally Posted by Angel Rox

Q1- The distance traveled by an object at time t ≥ 0 is s = f(t) = t^2 where s is in meter (m) and t in seconds (sec). Find the instantaneous velocity of the object at t = 2sec

Q2- Find the natural domain of the given function

h(x) = 1/1-sinx

Q3- What are the points of discontinuity for the function f(x)=x+5/x^2-1 ?

1) $f'(t)=2t$ plug in 2 get 4 $\frac{m}{s}$
2) $\sin(x)$ $\neq 1$ so $x \neq 0$
3) yes, $x=0$ is discontinuous

**Prove It** · December 11th 2008, 07:45 PM

Originally Posted by Erdos32212

1) $f'(t)=2t$ plug in 2 get 4 $\frac{m}{s}$
2) $\sin(x)$ $\neq 1$ so $x \neq 0$
3) yes, $x=0$ is discontinuous

3) Is the function $f(x) = \frac{x + 5}{x^2} - 1$ or $f(x) = \frac{x + 5}{x^2- 1}$ ?

**Angel Rox** · December 11th 2008, 08:00 PM

I cannot understand ur way of solving Mr.Erdos32212 ....

and for Sir.Prove It ...It is the 2ND one....

Plz I am in a hurry...

**Prove It** · December 11th 2008, 08:06 PM

Originally Posted by Angel Rox

I cannot understand ur way of solving Mr.Erdos32212 ....

and for Sir.Prove It ...It is the 2ND one....

Plz I am in a hurry...

The function is discontinuous when the denominator is 0.

So $x^2 - 1 = 0$

$x^2 = 1$

$x = \pm 1$

So the function is discontinuous at $x = \{-1, 1\}$ .

**Prove It** · December 11th 2008, 08:09 PM

Originally Posted by Angel Rox

Q1- The distance traveled by an object at time t ≥ 0 is s = f(t) = t^2 where s is in meter (m) and t in seconds (sec). Find the instantaneous velocity of the object at t = 2sec

Q2- Find the natural domain of the given function

h(x) = 1/1-sinx

Q3- What are the points of discontinuity for the function f(x)=x+5/x^2-1 ?

2. $h(x) = \frac{1}{1 - \sin{x}}$ .

This is a rational function, which is continuous everywhere except where the denominator is 0.

So it is discontinuous at

$1 - \sin{x} = 0$

$\sin{x} = 1$

$x = \frac{\pi}{2} + \pi n, n \in \mathbf{Z}$

So the natural domain is

$x \in \mathbf{R} \backslash \{\frac{\pi}{2} + \pi n, n \in \mathbf{Z}\}$

**Angel Rox** · December 11th 2008, 08:13 PM

Thanx alot Sir. I really appreciate ur way of solving and providing all the neccesary steps.

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