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If f(x)=|{:(x,x^(2),x^(3)),(1,2,3),(0,1,...

If f(x)=`|{:(x,x^(2),x^(3)),(1,2,3),(0,1,x):}|` `underset(x to1)limf(x)` is equal to

A

-1

B

0

C

1

D

2

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If F(x)=|{:(x,x^(2),x^(3)),(1,2x,3x^(2)),(0,2,6x):}| then F'(x) is equal to

    A
    `6x^(3)`
    B
    `x^(3)+6x^(2)`
    C
    3x
    D
    `6x^(2)`

  • If f(x)={{:(x,xlt1),(x-1,xge1):} , then underset(0)overset(2)intx^(2)f(x) dx is equal to :

    A
    1
    B
    `4/3`
    C
    `5/3`
    D
    `5/2`

  • Consider the following in respect of the function f(x)={{:(2+x,xge0),(2-x,xlt0):} 1. underset(xrarr1)limf(x) does not exist 2. f(x) is differentiable at x = 0 3. f(x) is continuous at x = 0 Which of the above statements is / are correct?

    A
    Only 1
    B
    Only 3
    C
    Both 2 and 3
    D
    Both 1 and 3

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    f'(x) = |{:(cos x , x , 1),(2sin x,x^(2),2x),(tan x, x,1):}| . The value of underset(x rarr 0)(lim) (f(x))/(x) is equal to

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