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"):}

If lim_(x rarr -3) (x^(k)+3^(k))/(x+3)=405 , where k is an odd natural number then, k = ________.

if 2x^(2) + 4x - k = 0 is same as (x-5) (x+k/10) = 0 , then find the value of k.

Evaluate, lim_(x to 1) (x^(4)-1)/(x-1)=lim_(x to k) (x^(3)-k^(3))/(x^(2)-k^(2)) , then find the value of k.

If lim_(x to 1) (x^(3) - 1)/(x - 1) = lim_(x to k) (x^(4) - k^(4))/(x^(3) - k^(3)) , find the value of k.

If lim_(x to 2) (x - 2)/(""^(3)sqrt(x) - ""^(3)sqrt(2)) = lim_(x to k) (x^(2) - k^(2))/(x - k) find the value of K

if log_(k)x.log_(5)k=log_(x)5,k!=1,k>0, then find the value of x

If (lim)_(x->oo)(7^(k x)+8)/(7^(5x)+6) does not exist then ' k ' can be

lim_(x to 0)[(1+3x)^(1//x)]=k , then k is