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Using Mathematical Induction Prove That `D/(Dx) (X^N) = Nx^(N -1)` For All Positive Integers N. - Mathematics

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प्रश्न

Using mathematical induction prove that  `d/(dx) (x^n) = nx^(n -1)` for all positive integers n.

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उत्तर

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पाठ 5: Continuity and Differentiability - Exercise 5.9 [पृष्ठ १९२]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 5 Continuity and Differentiability
Exercise 5.9 | Q 19 | पृष्ठ १९२

व्हिडिओ ट्यूटोरियलVIEW ALL [4]

संबंधित प्रश्‍न

Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = –3 and at x = 5.


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Find all points of discontinuity of f, where f is defined by:

f(x) = `{(2x + 3", if"  x<=2),(2x - 3", if"  x > 2):}`


Find all points of discontinuity of f, where f is defined by:

f(x) = `{(|x|+3", if"  x<= -3),(-2x", if" -3 < x < 3),(6x + 2", if"  x >= 3):}`


Find all points of discontinuity of f, where f is defined by:

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Find all points of discontinuity of f, where f is defined by:

f(x) = `{(x+1", if"  x>=1),(x^2+1", if"  x < 1):}`


Find all points of discontinuity of f, where f is defined by:

f(x) = `{(x^3 - 3", if"  x <= 2),(x^2 + 1", if"  x > 2):}`


Show that the function defined by g(x) = x − [x] is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x.


Find the points of discontinuity of f, where f(x) = `{(sinx/x", if"  x<0),(x + 1", if"  x >= 0):}`.


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Find the value of constant ‘k’ so that the function f (x) defined as

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is continous at x = -1


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Find the points of discontinuity, if any, of the following functions: \[f\left( x \right) = \begin{cases}2x , & \text{ if }  & x < 0 \\ 0 , & \text{ if }  & 0 \leq x \leq 1 \\ 4x , & \text{ if }  & x > 1\end{cases}\]


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Statement 2: The above graph is differentiable at x = 0

Which of the following is correct?


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