If g(x)=(1-a^x+x a^xloga)/(x^2*a^x), x<0...

If `g(x)=(1-a^x+x a^xloga)/(x^2*a^x), x<0` `((2a)^x-xlog(2a)-1)/(x^2), x >0` (where a > 0) then find a and `g(0)` so that `g(x)` is continuous at `x=0.`

Text Solution

Verified by Experts

The correct Answer is:

A, B

Topper's Solved these Questions

CONTINUITY
MOTION|Exercise EXERCISE - 3 (PASSAGE BASED QUESTION (21-24))|4 Videos
CONTINUITY
MOTION|Exercise EXERCISE - 4 (LEVEL -I) PREVIOUS YEAR JEE MAIN|4 Videos
CONTINUITY
MOTION|Exercise EXERCISE -2 (LEVEL -II) MIXED PROBLEMS|4 Videos
COMPLEX NUMBER
MOTION|Exercise EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED|33 Videos
DEFINITE INTEGRATION
MOTION|Exercise EXERCISE -4 LEVEL-II|33 Videos

Similar Questions

Explore conceptually related problems

If g(x)=(1-a^(x)+xa^(x)log a)/(x^(2)*a^(x)),x 0 (where a >0) then find a and g(0) so that g(x) is continuous at x=0.

Consider the function f(x)={(1-a^x+x a^x ln a)/(a^xx^2); x 0 where a > 0. If g(x) is continuous at x=0 then a=sqrt(2) (b) g(0)=1/8(ln2)^2 a=1/(sqrt(2)) (d) g(0)=1/2ln2

If f.g is continuous at x = 0 , then f and g are separately continuous at x = 0 .

Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g(x),x 0} Find g(x) such that f(x) is continuous and f'(1)=f(-1)

If f'(x)=g(x)(x-a)^(2), where g(a)!=0 and g is continuous at x=a, then :

Let f(x)=[x], where [.] is the greatest integer fraction and g(x)=sin x be two valued functions over R. Which of the following statements is correct? (a) Both f(x) and g(x) are continuous at x=0 (b) f(x) is continuous at x=0, but g(x) is not continuous at x=0. (c) g(x) is continuous at x=0, but f(x) is not continuous at x=0. (d) Both f(x) and g(x) are discontinuous at x=0

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

Let f and g be real valued functions defined on interval (-1, 1) such that g'' (x) is continuous, g(0) ne 0, g'(0) = 0, g''(0) ne 0, and f(x) = g''(0) ne 0 , and f(x) g(x) sin x . Statement I lim_( x to 0) [g(x) cos x - g(0)] [cosec x] = f''(0) . and Statement II f'(0) = g(0).

If (x)={g^(x),x =0f(x)={g^(x),x =0 where [.1) denotes the greatest integer function. The f(x)

Let f and g be real valued functions defined on interval (-1,\ 1) such that g"(x) is continuous, g(0)!=0 , g'(0)=0, g"(0)!=0 , and f(x)=g(x)sinx . Statement-1 : ("Lim")_(x->0)[g(x)cotx-g(0)"c o s e c"x]=f"(0) and Statement-2 : f'(0)=g(0)

MOTION-CONTINUITY -EXERCISE - 3

If the function f(x)=(3x^2+ax+a+3)/(x^2+x-2) is continuos at x=-2 .Fin...
Text Solution
|
Let f(x)=[(1-sinpix)/(1+cos2pix), x<1/2 and p , x=1/2 and sqrt(2x-1)...
Text Solution
|
If g(x)=(1-a^x+x a^xloga)/(x^2*a^x), x<0 ((2a)^x-xlog(2a)-1)/(x^2), x...
Text Solution
|
Let [x] denote the greatest integer function & f(x) be defined in a ne...
Text Solution
|
Let f(x) = [{:((pi/2.sin^(-1)(1-x^(2))sin^(-1(1-{x})))/(sqrt(2((x)-(x)...
Text Solution
|
Find all possible values of a and b so that f(x) is continous for all ...
Text Solution
|
Draw the graph of the function f(x) = x - |x - x^(2)|, -1 le x le 1 an...
Text Solution
|
Discuss the continuity of 'f' in [0, 2], where f(x) = {{:(|4x - 5|[x],...
Text Solution
|
let f(x)=(lncosx)/{(1+x^2)^(1/4)-1} if x > 0 and f(x)=(e^(sin4x)-1)/(l...
Text Solution
|
Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof)...
Text Solution
|
The function f(x)= ((2+ cos x)/(x^(3) sin x)-3/x^(4)) is not defined a...
Text Solution
|
The function f(x) = [{:((6/5)^(tan 6x)/(tan 5x), if, 0 lt x lt pi/2),(...
Text Solution
|
Determine a & b so that f is continuous at x = pi/2 whre f(x) = [{:(...
Text Solution
|
Determine the values of a , b , c for which the function f(x)={(sin(a+...
Text Solution
|
If f(x) = (Sin 3x + A sin 2x + B sinx)/x^5 for x != 0is continuous a...
Text Solution
|
A function f: RvecR is defined as f(x)=(lim)(nvecoo)(a x^2+b x+c+e^(n ...
Text Solution
|
Given the function g(x) = sqrt(6-2x) and h(x) = 2x^(2) - 3x + a. Then ...
Text Solution
|
f(x) = {{:((a^(sin x)-a^(tanx))/(tan x-sin x), "for",x gt 0),((ln(1+x+...
Text Solution
|
let f(x)=x^3-x^2-3x-1 , g(x)=(x+1)aand h(x)=f(x)/g(x) where h is a rat...
Text Solution
|