Question

lt x tends to 2. x^n -2^n /x-2=80 find n if n is a positive integer

Answer 1

$\lim_{x\to 2} \frac{x^n-2^n}{x-2}= 80$

This type of questions you can easily solve with help of L - Hospital rule .
because 0/0 is the form of limit .

now, use L - Hospital rule .
differentiate numerator and denominator separately with respect to x
you get , $\lim_{x\to 2} \frac{nx^{n-1}-0}{1}=80$
Now, put x = 2
$n(2)^{n-1}=80$

Now, factorize 80
factors of 80 = 2 × 2 × 2 × 2 × 5 = 5(2)⁴ = 5(2)⁽⁵⁻¹⁾

So, $n(2)^{n-1}=80 =5(2)^{5-1} \\\\ hence, n=5$

Answer 2

Step-by-step explanation:

hope it will be helpful for u all