Determine the intervals on which the given function is continuous: fx=x2+3x-10x-2, x≠210, - Maths - Limits and Derivatives

Question

Determine the intervals on which the given function is
continuous:
f x = x 2 + 3 x - 10 x - 2 ,     x ≠ 2 10 ,  
                 
                 
  x = 2
1 - ∞ , 2
2 2 , ∞
3 - ∞ , ∞
4 - ∞ , 2   a n d   2 , ∞

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

fx=x2+3x-10x-2x≠210x=2limx→2 x2+3x-10x-2= limx→2 x2+5x-2x-10x-2=limx→2 xx+5-2x+5x-2=limx→2 x+5x-2x-2=limx→2 x+5=2+5=7And f2=10Hence limx→2 fx≠f2Hence function us discontinous at x=2Hence function is continuous in -∞,2∪2,∞

Hope this information will clear your doubts about this topic

If you have any doubts just ask here on the ask and answer forum
and our experts will try to help you out as soon as possible
Regards

Determine the intervals on which the given function is continuous: f x = x 2 + 3 x - 10 x - 2 , x ≠ 2 10 , x = 2 1. - ∞ , 2 2. 2 , ∞ 3. - ∞ , ∞ 4. - ∞ , 2 a n d 2 , ∞

Determine the intervals on which the given function is continuous:
$f (x) = \{\begin{cases} \frac{x^{2} + 3 x - 10}{x - 2}, x \neq 2 \\ 10, x = 2 \end{cases}$
1. $(- \infty, 2)$
2. $(2, \infty)$
3. $(- \infty, \infty)$
4. $(- \infty, 2) a n d (2, \infty)$