Evaluate: `("lim")_(xvec0)(1+x)^(os e cx c)`

Evaluate: ("Lim")_(x->0^+)("c o s e c"x)^(1/(lnx))

Evaluate: ("lim")_(xvec2a^+)((e^x I n(2^(x-1))-(2^x-1)^xsinx)/(e^(x I nx)))^(1/x)

Evaluate: (lim)_(xvec 0)(log(5+x)-log(5-x))/(x)

The value of ("lim")_(xvec0)(e^(2x)-cos x-"ln"(1+2x))/(xtanx-sinx)i s 0 (b) 1 (c) 2 (d) 3

Evaluate: (lim)_(x rarr e)(log x-1)/(x-e)

Evaluate: lim_(x rarr0)(e^(x)-e^(x cos x))/((x+sin x))

If f(x)={("sin"[x])/([x]),for[x]!=0 0,for[x]=0,w h e r e[x] denotes the greatest integer less than or equal to x , then ("lim")_(xvec0)f(x) is 1 (b) 0 (c) -1 (d) none of these

If [.] is the greatest integer function and f(x)=[tan^2x], then (a) ("lim")_(xvec0)f(x) does not exist (b) f(x) is continuous at x=0 (c) f(x) is not differentiable at x=0 (d) f^(prime)(0)=1

Evaluate the limit: (lim)_(xvec 1)(sin(log x))/(log x)

Let f(x)={cos[x],xgeq0|x|+a ,x<0 The find the value of a , so that ("lim")_(xvec0) f(x) exists, where [x] denotes the greatest integer function less than or equal to x .