If f(x)={sinx ,x!=npi,n in I2,ot h e r ...

If `f(x)={sinx ,x!=npi,n in I2,ot h e r w i s e` `g(x)={x^2+1,x!=0,4,x=0 5,x=2` then `("lim")_(xvec0)g{f(x)}i s=`

`1`

`0`

`1/2`

`1/4`

Text Solution

Verified by Experts

The correct Answer is:

`lim_(xto0)g{f(x)}=lim_(xto0){f(x)}^(2)+1`
`=lim_(xto0)sin^(2)x+1=1`

Topper's Solved these Questions

PRACTICE SET 12
MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos
PRACTICE SET 14
MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

Similar Questions

Explore conceptually related problems

If f(x)={(sinx, x != npi " and " n in I_2), (2, " x=npi):} and g(x)={(x^2+1, x != 0),(4,x=0), (5, x=2):} then lim_(x->0) g{f(x)} is

If f(x)={x/(s in x),x >0 2-x ,xlt=0 and g(x)={x+3,x<1x^2-2x-2,1lt=x<2x-5,xgeq2 Then the value of (lim)_(xvec0)g(f(x)) a. is -2 b. is -3 c. is 1 d. does not exist

If f(x)={x-1,xgeq1 2x^2-2,x 0-x^2+1,xlt=0,a n dh(x) =|x|,t h e n("lim")_(xvec0)f(g(h(x))) is___

If f(x) = {{:(sin x"," x ne npi"," n = 0"," pm1"," pm2","...),(" 2, ""otherwise"):}} and g (x) ={{:(x^(2)+1"," x ne 0","2),(" 4, "x=0),(" 5, "x=2):}},"then" lim_(x to 0) g[f(x)] is ………

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

f(x)=[(sinx)/x ,"w h e n"x!=0=2,"w h e n"x=0 sinx-, when x0/(x) =L= 2, when x=0

Let f(x)={[x]x in I x-1x in I (where [.] denotes the greatest integer function) and g(x)={sinx+cosx ,x<0 1,xgeq0 . Then for f(g(x))a tx=0 (lim)_(xvec0)f(g(x)) exists but not continuous Continuous but not differentiable at x=0 Differentiable at x=0 (lim)_(xvec0)f(g(x)) does not exist f(x) is continuous but not differentiable

If f(x)=(3x^2+a x+a+1)/(x^2+x-2), then which of the following can be correct ("lim")_(xvec1)f(x)e xi s t s a=-2 ("lim")_(xvec-2)f(x)e xi s t s a=13 ("lim")_(xvec1)f(x)=4/3 ("lim")_(xvec-2)f(x)=-1/3

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 13-PAPER II OBJECTIVE TYPE

The switching function of network is
Text Solution
|
A five digit number is formed but the digits 1,2,3,4,5 without repetit...
Text Solution
|
If f(x)={sinx ,x!=npi,n in I2,ot h e r w i s e g(x)={x^2+1,x!=0,4,x=...
Text Solution
|
If f(x)=log(x)(log(e)x), then f'(x)at x=e is equal to
Text Solution
|
The value of lim(x->a)log(x-a)/(log(e^x-e^a) is
Text Solution
|
if 2^x+2^y=2^(x+y) then the value of (dy)/(dx) at x=y=1
Text Solution
|
intx^(3)log x dx is equal to
Text Solution
|
The value of int(2)^(3)(x+1)/(x^(2)(x-1))dx is
Text Solution
|
if |veca|=4, |vecb|=2 and the angle between veca and vecb is pi/6 th...
Text Solution
|
The differential equation of the rectangular hyperbola whose axes are ...
Text Solution
|
The statement pvv~p is
Text Solution
|
If birth to amale child and birth to a femal child are equal probable,...
Text Solution
|
If y=tan^(-1)[(sinx+cosx)/(cosx-sinx)] then (dy)/(dx) is
Text Solution
|
The equation 12x^(2)+7xy-12y^(2)-18x+y+6=0 represents
Text Solution
|
A focus of an ellipse is at the origin. The directrix is the line x=4 ...
Text Solution
|
A parabola is drawn with focus at (3,4) and vertex at the focus of the...
Text Solution
|
If a circle passes through (0,0) and (a,0) and (0,b), then the coordin...
Text Solution
|
A line is drawn through the point P(3,11) to cut the circle x^(2)+y^(2...
Text Solution
|
If the first, second and last terms of an arithmetic series are a,b, a...
Text Solution
|
The denominator of a fraction is greater than 16 of the square of nume...
Text Solution
|