Test: Limits And Continuity : Intuitive Approach - 3

 is equal to 

If f(x) = x for  0 ≤ x 1/2, f(x) = 1 for x = 1-x for 1/2<x<1 then at x =1/2 the function is 

e^-1/x[1+e^1/x]^-1 is

If f(x)=9x÷(x+2) for x<1, f(1)=3, f(x)=(x+3)x-1 for x>1, then in the interval (-3,3) the function is

Function f(x) = K.x-1  for x < 2
                   = x-k     for x ≥ 2
is continuous at x = 2
The value of 'k' is __________.

Evaluate 

Evaluate

The points of discontinuity of the function, F(x) =  are 

Find limn→∞(2n-1)2ⁿ (2n+1)^-1 2^1-n

Find lim_n→∞[4n² + 6n +2] ÷ 4n²

Find lim_n→∞[xⁿ.(n+1)] ÷ [nx ⁿ⁺¹ ]

 Find lim_n→∞[n(n+2)] ÷ (n+1)²

Find lim_n→∞(n³ +a )[(n+1)³a]^-1 (2ⁿ⁺¹ +a ) (2ⁿ +a)^-1

Find lim_n→∞(n² +1)[(n+1)² +1]^-1 5ⁿ⁺¹ 5^-n

Find lim_n→∞nⁿ(n+1)^-n-1 ÷ n^-1

Find lim_n→∞2^n-1 (10 +n) (9+n)^-1 2^-n

Find lim_n→∞(1+n^-1)[1+2n)^-1]^-1

Find lim_n→∞[nⁿ. (n+1)!] ÷ [n! (n+1)ⁿ⁺¹]

 Find lim_n→∞[(n+1)ⁿ⁺¹. n^-n-1 -(n+1).n^-1]^-n

 3x²+2x-1 is continuous

 Find lim_n→∞nⁿ (1+n)^-n

 Find lim_n→∞[n!3ⁿ⁺¹] ÷[3ⁿ(n+1)!]

The value of the limit when x tends to zero of the expression (1+n)^1/n is 

The value of the limit when x tends to zero of the expression (1+n)^1/n is

The value of the limit when x tends to zero of the expression [(1+x)ⁿ-1] ]

The value of the limit when x tends to 2 of the expression (x-2)^-1-(x²-3x+2)^-1 is

The value of the limit when x tends to zero of the expression (e^x-1)/x is 

The value of the limit when n tends to infinity of the expression 2^-n(n²+5n+6)[(n+4)(n+5)]^-1 is

The value of the limit when x tends to zero of the expression (1+n)^1/n is 

Find  lim_n→∞[n^1/2 + (n+1)^1/2]^-1 ÷ n^-1/2 

The value of the limit when x tends to zero of the expression [(a+x²)^1/2 

 Find lim_n→∞ (2ⁿ-2)(2ⁿ+1)^-1

 Find lim_n→∞ [(n³ +1)^1/2 - n ^{3/2] ÷ n3/2}