If `lim_(x->5) (x^k-5^k)/(x-5)=500` then find `k`

If lim_(x rarr5)(x^(k)-5^(k))/(x-5)=500 then find k

Match the following : {:("Column I ", " Column II" ), ("(A)" if lim_(x to 1) (1-x) tan""(pix)/2 = k " then " sin (1/k) " is" , "(p)"4),( "(B)" if lim_(x to 5) (x^(k)-5^(k))/(x-5) = 500 " then k is " , "(q)" 1),("(C)" lim_(x to oo)(1 + 4/(x+1))^((3x-1)/3) " is equal to " e^(k) " , then k is" , "(r) A perfect sqare"), ("(D) " d^(20)/(dx^(20)) (2 cos x"," cos 3x)= 2^(4k) [ cos2x + 2^(20) . cos4k]" then k is " , "(s)" 5),(, "(t)An odd number"):}

Match the following : {:("Column I ", " Column II" ), ("(A)" if lim_(x to 1) (1-x) tan""(pix)/2 = k " then " sin (1/k) " is" , "(p)"4),( "(B)" if lim_(x to 5) (x^(k)-5^(k))/(x-5) = 500 " then k is " , "(q)" 1),("(C)" lim_(x to oo)(1 + 4/(x+1))^((3x-1)/3) " is equal to " e^(k) " , then k is" , "(r) A perfect sqare"), ("(D) " d^(20)/(dx^(20)) (2 cos x"," cos 3x)= 2^(4k) [ cos2x + 2^(20) . cos4k]" then k is " , "(s)" 5),(, "(t)An odd number"):}

If underset (x rarr 5)lim (x^k-5^k)/(x-5)=500 ,then find the positive value of k.

If lim_(x rarr 5)((x^k - 5^k)/(x - 5)) = 500 , then k is equal to

2x+5=K then x=

If lim_(x->oo)(x^2+3x+5)/(4x+1+x^k) exists then K (a) k =2 (b) k 2 (d) k >=2