Home
Class 12
MATHS
Consider f(x) = {{:(2 sin (a cos^(-1) x)...

Consider `f(x) = {{:(2 sin (a cos^(-1) x)",","if",x in (0, 1)),(sqrt(3)",","if",x = 0),(ax + b",","if",x lt 0):}`
Statement I If b = `sqrt(3) and a = (2)/(3)`, then f(x) is continuous in `(-oo, 1)`.
Statement II If a function is defined on an interval I and limit exists at every point of interval I, then function is continuous in I.

A

Statement I is correct, Statement II is also correct, Statement II is the correct explanation of Statement I

B

Statement I is correct, Statement II is also correct, Statement II is not the correct explanation of Statement I

C

Statement I is correct, Statement II is incorrect

D

Statement I is incorrect, Statement II is correct.

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise EXERCISE 4|3 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

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

Let f(x) = {{:(Ax - B",",x le -1),(2x^(2) + 3Ax + B",",-1 lt x le 1),(4",",x gt 1):} Statement I f(x) is continuous at all x, if A = (3)/(4) . Statement II Polynomial function is always continuous.

If f(x)=x^(2)"sin"(1)/(x) , where xne0 then the value of the function f at x=0, so that the function is continuous at x=0, is

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

If f(x) = sqrt((1)/(tan^(-1)(x^(2)-4x + 3))) , then f(x) is continuous for a. (1, 3) b. (-oo, 0) c. (-oo, 1) uu (3, oo) d. None of these

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

If function f(x) = (sqrt(1+x) - root(3)(1+x))/(x) is continuous function at x = 0, then f(0) is equal to

If the function f is defined by f(x) = {(3,,x,ne,0),(a+1,,x,=,0):} and f is continuous at x = 0, then value of a is :

Consider the piecewise defined function f(x) = {{:(sqrt(-x),"if",x lt 0),(0,"if",0 le x le 4),(x - 4,"if",x gt 4):} describe the continuity of this function.

Statement I If f (x) = int_(0)^(1) (xf(t)+1) dt, then int_(0)^(3) f (x) dx =12 Statement II f(x)=3x+1