If `f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0` and `f(0)=1` is continuous at `x=0` then the value of `m+n` is a. 2 b. 3 c. -3 d. 7

If f(x)=(acos x-cos b x)/(x^2),x!=0a n df(0)=4 is continous at x=0, then the ordered pair (a ,b) is (+-1,3) b. (1,+-3) c. (-1,-3) d. (-1,3)

If f(x)={(cos^2x-sin^2x-1)/(sqrt(x^2+1)-1), x!=0,and f(x)=k , x=0" is continuous at "x=0,"find " k

If f(x)={(sin((2x^2)/a)+cos((3x)/b))^((ab)/x^2),x!=0, and e^3, x=0 is continuous at x=0AAb in R then minimum value of a is a. -1//8 b. -1//4 c. -1//2 d. 0

The function f(x)=((3^x-1)^2)/(sinx*ln(1+x)), x != 0, is continuous at x=0, Then the value of f(0) is

If f(x)=(sin^(- 1)x)^2*cos(1/ x)"if"x!=0;f(0)=0,f(x) is continuous at x= 0 or not ?

If f(x)={(sin((2x^2)/a)+cos((3x)/b))^(ab//x^2),x!=0 & e^3 at x=0} is continuous at x=0AAb in R then minimum value of a is -1//8 b. -1//4 c. -1//2 d. 0

Let f(x)= {(((xsinx+2cos2x)/(2))^((1)/(x^(2))),,,,xne0),(e^(-K//2),,,,x=0):} if f(x) is continous at x=0 then the value of k is (a) 1 (b) 2 (c) 3 (d) 4

Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):} . If f(x) is continuous at x=0 then the value of alpha^2+beta^2 is

If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is continuous at x=0 , then the value of a/b is (A) 3/5f(0) (B) 2^(8/5)f(0) (C) (64)/5f(0) (D) none of these

If f(x)={(1-cos10 x)/(x^2) , x 0 , then the value of a so that f(x) may be continuous at x=0 , is (a) 25 (b) 50 (c) -25 (d) none of these