If displaystyle limx → 5 (xk - 5k/x - 5) = 500 then k is equal to :

Question

If displaystyle limx → 5 (xk - 5k/x - 5) = 500 then k is equal to : (A) 3 (B) 4 (C) 5 (D) 6

Tardigrade Admin · Accepted Answer

Let displaystyle limx → 5 (xk - 5k/x - 5) = 500 By using displaystyle limx → a (xn - an/x - a) = n.an -1 we have k.5k -1 = 500 Now, put k = 4, we get 4.54 -1 = 500 ⇒ : : 4.53 = 500 which is ture. ∴ : :: k = 4

Q. If $x \to 5 lim \frac{x ^{k} - 5 ^{k}}{x - 5} = 500$ then k is equal to :

3

4

5

6

Let $x \to 5 lim \frac{x ^{k} - 5 ^{k}}{x - 5} = 500$
By using $x \to a lim \frac{x ^{n} - a ^{n}}{x - a} = n . a^{n - 1}$ we have $k . 5^{k - 1} = 500$
Now, put $k = 4$ , we get
$4. 5^{4 - 1} = 500$
$\Rightarrow 4. 5^{3} = 500$ which is ture.
$∴ k = 4$

Q. If x→5lim​x−5xk−5k​=500 then k is equal to :

3

4

5

6

Let x→5lim​x−5xk−5k​=500 By using x→alim​x−axn−an​=n.an−1 we have k.5k−1=500 Now, put k=4, we get 4.54−1=500 ⇒4.53=500 which is ture. ∴k=4

Q. If $x \to 5 lim \frac{x ^{k} - 5 ^{k}}{x - 5} = 500$ then k is equal to :

Let $x \to 5 lim \frac{x ^{k} - 5 ^{k}}{x - 5} = 500$
By using $x \to a lim \frac{x ^{n} - a ^{n}}{x - a} = n . a^{n - 1}$ we have $k . 5^{k - 1} = 500$
Now, put $k = 4$ , we get
$4. 5^{4 - 1} = 500$
$\Rightarrow 4. 5^{3} = 500$ which is ture.
$∴ k = 4$