Let `L_1=(lim)_(xvec4)(x-6)^x n dL_2=(lim)_(xvec4)(x-6)^4dot` Which of the following is true? Both `L_1a n dL_2` exists Neither `L_1a n dL_2` exists `L_1` exists but `L_2` does not exist `L_2` exists but `L_1` does not exist

Let L_(1)=lim_(xrarr4) (x-6)^(x)and L_(2)=lim_(xrarr4) (x-6)^(4) . Which of the following is true?

Consider the function f(x) =[(1-x,0 leq x leq 1),(x+ 2, 1 lt x lt 2),(4-x,2 leqxleq4)). Let lim_(x->1) f(f(x))= l and lim_(x->1) f(f(x))=m then which one of the following hold good ? (A) l exist but m does not (B) m exist but l does not (C) both exist (D) both does not exist

To show that lim_( x to 1)"sin"1/(x-1) does not exist.

Show that (lim)_(x rarr0)(1)/(2) does not exist.

Show that lim_(xrarr2) ([x-2])/(x-2) does not exist.

Consider the following graph of the function y=f(x). Which of the following is//are correct? (a) lim_(xto1) f(x) does not exist. (b) lim_(xto2)f(x) does not exist. (c) lim_(xto3) f(x)=3. (d)lim_(xto1.99) f(x) exists.

Let lim_(x rarr0)([x]^(2))/(x^(2))=l and lim_(x rarr0)([x^(2)])/(x^(2))=m where [.] denotes greatest integer.Then (a)l exists but m does not (b) m exists but l does not (c)both 1 and m exist (d) neither ln or m exists

Let L_(1)=(x+3)/(-4)=(y-6)/(3)=(z)/(2) and L_(2)=(x-2)/(-4)=(y+1)/(1)=(z-6)/(1) Which of these are incorrect? (A) L_(1), L_(2) are coplanar. (B) L_(1),L_(2) are skew lines (C) Shortest distance between L_(1),L_(2) is 9 (D) (hat i-4hat j+8hat k) is a vector perpendicular to both L_(1),L_(2)

Consider the following : 1. lim_(xto0) (1)/(x) exists. 2. lim_(xto0) (1)/(e^(x)) does not exist. Which of the above is/are correct?

Consider the following statements: 1. lim_(xto0)sin""(1)/(x) does not exist. 2. lim_(xto0)sin""(1)/(x) exists. Which of the above statements correct?