Home
Class 12
MATHS
Let f(x) = {{:((a(1-x sin x)+b cos x + 5...

Let `f(x) = {{:((a(1-x sin x)+b cos x + 5)/(x^(2))",",x lt 0),(3",",x = 0),([1 + ((cx + dx^(3))/(x^(2)))]^(1//x)",",x gt 0):}` If f is continuous at x = 0, then (a + b + c + d) is

A

[-10,10]

B

[-5,5]

C

[-12,12]

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f (x)=[{:((a (1-x sin x)+ b cos x +5)/(x ^(2)),,, x lt 0), ((1+ ((dx + dx ^(3))/(dx ^(2))))^(1/x),,, x gt 0):} If f is continous at x=0 then correct statement (s) is/are:

Let f (x)=[{:((a (1-x sin x)+ b cos x +5)/(x ^(2)),,, x lt 0), ((1+ ((dx + dx ^(3))/(dx ^(2))))^(1/x),,, x gt 0):} If f is continous at x=0 then correct statement (s) is/are:

F(x) = {( (sin(a+2)x + sin x)/x , x lt 0), (b , x = 0), (((x + 3x^2 )^(1/3) - x^(1/3))/x^(4/3)), x gt 0):} Function is continuous at x = 0, find a + 2b .

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

Consider f(x) = {{:((8^(x) - 4^(x) - 2^(x) + 1)/(x^(2))",",x gt 0),(e^(x)sin x + pi x + k log 4",",x lt 0):} Then, f(0) so that f(x) is continuous at x = 0, is

If f(x) = {{:(((pi)/(2)-sin^(-1)(1-{x}^(2))sin^(-1)(1-{x}))/(sqrt(2) ({x} - {x}^(3)))",",x gt 0),(k",",x = 0),((A sin^(-1)(1-{x})cos^(-1)(1-{x}))/(sqrt(2{x})(1-{x}))",",x lt 0):} is continuous at x = 0, then the value of sin^(2) k + cos^(2) ((Api)/(sqrt(2))) , is..... (where {.} denotes fractional part of x).

Let f (x)= {((1+ax )^(1//x), x lt 0),( ((x+c)^(1//3)-1)/((x+1)^(1//2) -1), x gt 0):}, is continous at x=0, then 3 (e ^(a)+b+c) is equal to:

If the function f(x) defined as f(x) defined as f(x)={3,x=0(1+(a x+b x^3)/(x^2))^(1/x),x >0 is continuous at x=0, then a=0 b. b=e^3 c. a=1 d. b=(log)_e3

Let the function f(x)=x^(2)sin((1)/(x)), AA x ne 0 is continuous at x = 0. Then, the vaue of the function at x = 0 is

Let f(x) = {{:({1 + |sin x|}^(a//|sin x|)",",-pi//6 lt x lt 0),(b",",x = 0),(e^(tan 2x//tan 3x)",",0 lt x lt pi//6):} Determine a and b such that f(x) is continuous at x = 0