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Is it true that x=e^(logx) for all real...

Is it true that `x=e^(logx)` for all real

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`y=e^ logx`
For `x=0, y=e ^ log0`
But log0 is not defined. ...
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Knowledge Check

  • Which statements is true for all real values of x and y?

    A
    `(x+y)^(2)=x^(2)+y^(2)`
    B
    `x^(2)+x^(2)=x^(4)`
    C
    `(2^(x+2))/(2^(x))=4`
    D
    `(2^(x+2))/(2^(x))=-4`
    • NCERT ENGLISH-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES
    1. Is it true that x=e^(logx) for all real

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    2. Differentiate the following w.r.t. x:(i) e^(-x) (ii) sin (log x), x &g...

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    3. Show that the function f defined by f(x)=|1-x+x|, where x is any real...

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    4. Find the derivative of the function given b y f(x) = sin(x^2)dot

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    5. Find the derivative of tan (2x + 3).

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    6. Differentiate sin(cos(x^2)) with respect to x.

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    7. Find (dy)/(dx)if x-y =pi

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    8. Find (dy)/(dx), if y + siny = cosx

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    9. Find the derivative of f given by f(x)=sin^(-1)xassuming it exists.

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    10. Find the derivative of / given by f(x)=tan^(-1)xassuming it exists.

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    11. Find df/dx if f(x) = (sin x) ^ sin x for all o lt x lt pi .

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    12. Differentiate sin^2xw.r.t e^(cosx).

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    13. Differentiate the following w.r.t x.(i) sqrt(3x+2)+(1/(sqrt(2x^2 + 4))...

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    14. Find f'(x)if f(x)=(sinx)^(sinx)for all 0<x<pi

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    15. Verify Rolles theorem for the function y=x^2+2,a=-2and b = 2.

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    16. Verify the Mean Value Theorm for f(x)=x^2 in the interval [2,4].

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    17. If y=3e^(2x)+2e^(3x). Prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0.

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    18. If y=sin^(-1)x, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0.

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    19. Find all the points of discontinuity of the function f defined byf(x)...

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    20. Discuss the continuity of the function f defined byf(x)={x+2ifxlt=1 x-...

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